Authors:Zhen-Qing Chen; Xicheng Zhang Pages: 1 - 21 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Zhen-Qing Chen, Xicheng Zhang When studying non-symmetric nonlocal operators on R d : L f ( x ) = ∫ R d ( f ( x + z ) − f ( x ) − ∇ f ( x ) ⋅ z 1 { z ⩽ 1 } ) κ ( x , z ) z d + α d z , where 0 < α < 2 , d ⩾ 1 , and κ ( x , z ) is a function on R d × R d that is bounded between two positive constants, it is customary to assume that κ ( x , z ) is symmetric in z. In this paper, we study heat kernel of L and derive its two-sided sharp bounds without the symmetric assumption κ ( x , z ) = κ ( x , − z ) . In fact, we allow the kernel κ to be time-dependent and x → κ ( t , x , z ) to be only locally β-Hölder continuous with Hölder constant possibly growing at a polynomial rate in z . We also derive gradient estimate when β ∈ ( 0 ∨ ( 1 − α ) , 1 ) as well as fractional derivative estimate of order θ ∈ ( 0 , ( α + β ) ∧ 2 ) for the heat kernel. Moreover, when α ∈ ( 1 , 2 ) , drift perturbation of the time-dependent non-local operator L t with drift in Kato's class is also studied in this paper. As an application, when κ ( x , z ) = κ ( z ) does not depend on x, we show the boundedness of nonlocal Riesz's transformation: for any p > 2 d / ( d + α ) , ‖ L 1 / 2 f ‖ p... PubDate: 2018-05-31T15:28:02Z DOI: 10.1016/j.jmaa.2018.03.054

Authors:Habiba Kadiri; Allysa Lumley; Nathan Ng Pages: 22 - 46 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Habiba Kadiri, Allysa Lumley, Nathan Ng Let N ( σ , T ) denote the number of nontrivial zeros of the Riemann zeta function with real part greater than σ and imaginary part between 0 and T. We provide explicit upper bounds for N ( σ , T ) commonly referred to as a zero density result. In 1937, Ingham showed the following asymptotic result N ( σ , T ) = O ( T 8 3 ( 1 − σ ) ( log T ) 5 ) . Ramaré recently proved an explicit version of this estimate. We discuss a generalization of the method used in these two results which yields an explicit bound of a similar shape while also improving the constants.

Authors:Long Bai; Krzysztof Dȩbicki; Peng Liu Pages: 47 - 74 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Long Bai, Krzysztof Dȩbicki, Peng Liu Let X ( t ) = ( X 1 ( t ) , … , X n ( t ) ) , t ∈ T ⊂ R be a centered vector-valued Gaussian process with independent components and continuous trajectories, and h ( t ) = ( h 1 ( t ) , … , h n ( t ) ) , t ∈ T be a vector-valued continuous function. We investigate the asymptotics of P { sup t ∈ T min 1 ≤ i ≤ n ( X i ( t ) + h i ( t ) ) > u } as u → ∞ . As an illustration to the derived results we analyze two important classes of X ( t ) : with locally-stationary structure and with varying variances of the coordinates, and calculate exact asymptotics of simultaneous ruin probability and ruin time in a Gaussian risk model.

Authors:Adam Kubica; Katarzyna Ryszewska Pages: 75 - 99 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Adam Kubica, Katarzyna Ryszewska We consider the decay of solution to a fractional diffusion equation with distributed order Caputo derivative. We assume that the elliptic operator is time-dependent and that the weight function, contained in the definition of the distributed order Caputo derivative, is just integrable. We establish the relation between behavior of the weight function near zero and the decay rate of solution.

Authors:Piermarco Cannarsa; Alexander Khapalov Pages: 100 - 124 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Piermarco Cannarsa, Alexander Khapalov We study the local controllability properties of generic 2-D and 3-D bio-mimetic swimmers employing the change of their geometric shape to propel themselves in an incompressible fluid described by the Navier–Stokes equations. It is assumed that swimmers' bodies consist of finitely many parts, identified with the fluid they occupy, that are subsequently linked by the rotational and elastic internal forces. These forces are explicitly described and serve as the means to affect the geometric configuration of swimmers' bodies. Similar models were previously introduced and investigated in [3–10].

Authors:Frédéric Bayart; Udayan B. Darji; Benito Pires Pages: 125 - 139 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Frédéric Bayart, Udayan B. Darji, Benito Pires Let X = ( X , B , μ ) be a σ-finite measure space and f : X → X be a measurable transformation such that the composition operator T f : φ ↦ φ ∘ f is a bounded linear operator acting on L p ( X , B , μ ) , 1 ≤ p < ∞ . We provide a necessary and sufficient condition on f for T f to be topologically transitive or topologically mixing. We also characterize the topological dynamics of composition operators induced by weighted shifts, non-singular odometers and inner functions. The results provided in this article hold for composition operators acting on more general Banach spaces of functions.

Authors:Fubao Zhang; Hui Zhang Pages: 159 - 174 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Fubao Zhang, Hui Zhang In this paper, we are concerned with the following Choquard equation in R 3 that − ϵ 2 Δ u + V ( x ) u = ϵ μ − 3 [ ( ∫ R 3 P ( y ) u ( y ) p x − y μ ) P ( x ) u p − 2 u + ( ∫ R 3 Q ( y ) u ( y ) q x − y μ ) Q ( x ) u q − 2 u ] , where ϵ > 0 is a parameter, 0 < μ < 3 , 6 − μ 3 < q < p < 6 − μ , the functions V and P are positive and Q may be sign-changing. Via variational methods, we establish the existence of ground states for small ϵ, and investigate the concentration behavior of ground states and show that they concentrate at a global minimum point of the least energy function as ϵ → 0 .

Authors:Evandro Raimundo da Silva Pages: 175 - 195 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Evandro Raimundo da Silva We show local solvability in Besov spaces for a class of first order linear operators L defined on an open set of R n + 1 , n ∈ N , satisfying the condition (P) of Nirenberg–Treves and whose coefficients are Hölder continuous. Moreover, when n = 1 , we show local solvability for L in L ∞ ( R , B ∞ , ∞ s ( R ) ) , B ∞ , ∞ s ( R 2 ) and L q ( R , B p , q s ( R ) ) , 1 < p < ∞ , 1 ≤ q ≤ ∞ , s ∈ R . Recalling that C s = B ∞ , ∞ s , if s > 0 and not an integer (Hölder space), then we have local solvability for L in L ∞ ( R , C s ( R ) ) and C s ( R 2 ) .

Authors:Hidetaka Hamada Pages: 196 - 210 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Hidetaka Hamada In this paper, we prove a Schwarz lemma at the boundary for holomorphic self-mappings f of finite dimensional irreducible bounded symmetric domains without assuming the boundary regularity of f. Our result generalizes the previous results obtained for holomorphic self-mappings f of the Euclidean unit ball, or of the classical Cartan domains of type I and of type II which are smooth up to the boundary.

Authors:Chiara Bianchini; Giulio Ciraolo; Paolo Salani Pages: 211 - 219 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Chiara Bianchini, Giulio Ciraolo, Paolo Salani We characterize the Wulff shape of an anisotropic norm in terms of solutions to overdetermined problems for the Finsler p-capacity of a convex set Ω ⊂ R N , with 1 < p < N . In particular we show that if the Finsler p-capacitary potential u associated to Ω has two homothetic level sets then Ω is Wulff shape. Moreover, we show that the concavity exponent of u is q = − ( p − 1 ) / ( N − p ) if and only if Ω is Wulff shape.

Authors:Changjian Liu; Guoting Chen; Zhongqin Sun Pages: 220 - 234 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Changjian Liu, Guoting Chen, Zhongqin Sun New criteria to determine the monotonicity of the ratio of two Abelian integrals are given. When two Abelian integrals have the forms ∫ Γ h f 1 ( x ) y d x and ∫ Γ h f 2 ( x ) y d x or the forms ∫ Γ h f 1 ( x ) y d x and ∫ Γ h f 2 ( x ) y d x and Γ h are ovals belonging to the level set { ( x , y ) H ( x , y ) = h } , where H ( x , y ) has the form y 2 / 2 + Ψ ( x ) or ϕ ( x ) y 2 / 2 + Ψ ( x ) , we give new criteria, which are defined directly by the functions which appear in the above Abelian integrals, and prove that the monotonicity of the criteria implies the monotonicity of the ratios of the Abelian integrals. The new criteria are applicable in a large class of problems, some of which simplify the existing proofs and some of which generalize known results.

Authors:Maciej Ciesielski Pages: 235 - 258 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Maciej Ciesielski In this paper we investigate a relationship between fully k-rotundity properties, uniform K-monotonicity properties, reflexivity and K-order continuity in symmetric spaces E. We also answer a crucial question whether fully k-rotundity properties might be restricted in definition to E d the positive cone of all nonnegative and decreasing elements of E. We present a complete characterization of decreasing uniform K-monotonicity and K-order continuity in E. It is worth mentioning that we also establish several auxiliary results describing reflexivity in Lorentz spaces Γ p , w and K-order continuity in Orlicz spaces L ψ . Finally, we show an application of discussed geometric properties to the approximation theory.

Authors:P. Del Moral; A. Niclas Pages: 259 - 266 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): P. Del Moral, A. Niclas This short note provides an explicit description of the Fréchet derivatives of the principal square root matrix function at any order. We present an original formulation that allows to compute sequentially the Fréchet derivatives of the matrix square root at any order starting from the first order derivative. A Taylor expansion at any order with an integral remainder term is also provided, yielding the first result of this type for this class of matrix function.

Authors:Ibrahim Halil Gümüş; Hamid Reza Moradi; Mohammad Sababheh Pages: 267 - 280 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Ibrahim Halil Gümüş, Hamid Reza Moradi, Mohammad Sababheh Our main target in this paper is to present new sharp bounds for inequalities that result when weighted operator means are filtered through positive linear maps and operator monotone functions. As an application, we prove a refined reverse of the celebrated Golden–Thompson inequality. Furthermore, we show how these inequalities can be squared.

Authors:Yinxia Wang; Ling Xue Pages: 281 - 296 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Yinxia Wang, Ling Xue In this paper, we investigate the generalized double dispersion equation with periodic external force in R n . We prove the existence and uniqueness of time periodic solutions that have the same period as the external force in some suitable function space for the space dimension n ≥ 3 . The proof is based on the spectral analysis for the solution operator and the contraction mapping theorem. In addition, we also discuss the time asymptotic stability of the time periodic solutions by continuous argument.

Authors:J. Ferrer; E. Llorens-Fuster Pages: 297 - 308 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): J. Ferrer, E. Llorens-Fuster We find lower bounds for the set of Lipschitz constants of a given Lipschitzian map, defined on the closed unit ball of a Hilbert space, with respect to any renorming. We introduce a class of maps, defined in the closed unit ball of ℓ 2 , which contains the classical fixed point free maps due to Goebel–Kirk–Thelle, Baillon, and P.K. Lin. We show that for any map of this class its uniform Lipschitz constant with respect to any renorming of ℓ 2 is never strictly less than π 2 .

Authors:Liliana Cely; Elói M. Galego; Manuel González Pages: 309 - 317 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Liliana Cely, Elói M. Galego, Manuel González We study the convolution operators T μ acting on the group algebras L 1 ( G ) and M ( G ) , where G is a locally compact abelian group and μ is a complex Borel measure on G. We show that a cotauberian convolution operator T μ acting on L 1 ( G ) is Fredholm of index zero, and that T μ is tauberian if and only if so is the corresponding convolution operator acting on the algebra of measures M ( G ) , and we give some applications of these results.

Authors:Yuzhu Wang; Changhua Wei Pages: 318 - 330 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Yuzhu Wang, Changhua Wei In this paper, we introduce a new concept of completely linear degeneracy for quasilinear hyperbolic systems in several space variables, and then get an interesting property for multidimensional hyperbolic conservation laws satisfying our new definition. For applications, we give some examples arising from mathematics and physics at last.

Authors:Yehonatan Salman Pages: 331 - 347 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Yehonatan Salman The aim of the article is to generalize the method presented in [3, Theorem 1] by G. Ambartsoumian, R. Gouia-Zarrad and M. Lewis for recovering functions from their spherical mean transform with limited radii data from the two dimensional case to the general n dimensional case. The idea behind the method is to expand each function in question into spherical harmonics and then obtain, for each term in the expansion, an integral equation of Volterra's type that can be solved iteratively. We show also how this method can be modified for the spherical case of recovering functions from the spherical transform with limited radii data. Lastly, we solve the analogous problem for the case of the Funk transform by again using expansion into spherical harmonics and then obtain an Abel type integral equation which can be inverted by a method introduced in [14].

Authors:Thu Hien Nguyen; Anna Vishnyakova Pages: 348 - 358 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Thu Hien Nguyen, Anna Vishnyakova For an entire function f ( z ) = ∑ k = 0 ∞ a k z k , a k > 0 , we show that f belongs to the Laguerre–Pólya class if the quotients a n − 1 2 / a n − 2 a n are decreasing in n, and b : = lim n → ∞ a n − 1 2 / a n − 2 a n such that b ≥ q ∞ ( q ∞ ≈ 3 . 2336 ) . This estimation is sharp.

Authors:Stefano Bonaccorsi; Adrian Zălinescu Pages: 359 - 378 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Stefano Bonaccorsi, Adrian Zălinescu We study a control problem where the state equation is a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise. We allow the control to act on the boundary and set boundary conditions which result in a stochastic differential equation for the trace of the solution on the boundary. This work provides necessary and sufficient conditions of optimality in the form of a maximum principle. We also provide a result of existence for the optimal control in the case where the control acts linearly.

Authors:Pedro T. P. Lopes; Marcone C. Pereira Pages: 379 - 402 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Pedro T. P. Lopes, Marcone C. Pereira In this paper, we study existence, uniqueness and asymptotic behavior of the Laplace equation with dynamical boundary conditions on regular non-cylindrical domains. We write the problem as a non-autonomous Dirichlet-to-Neumann operator and use form methods in a more general framework to accomplish our goal. A class of non-autonomous elliptic problems with dynamical boundary conditions on Lipschitz domains is also considered in this same context.

Authors:Karen Yagdjian; Andras Balogh Pages: 403 - 422 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Karen Yagdjian, Andras Balogh In this article we discuss the maximum principle for the linear equation and the sign changing solutions of the semilinear equation with the Higgs potential. Numerical simulations indicate that the bubbles for the semilinear Klein–Gordon equation in the de Sitter space–time are created and apparently exist for all times.

Authors:Arran Fernandez; Athanassios S. Fokas Pages: 423 - 458 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Arran Fernandez, Athanassios S. Fokas We present several formulae for the large-t asymptotics of the modified Hurwitz zeta function ζ 1 ( x , s ) , x > 0 , s = σ + i t , 0 < σ ≤ 1 , t > 0 , which are valid to all orders. In the case of x = 0 , these formulae are consistent with the asymptotic expressions recently obtained for the Riemann zeta function, which include the classical results of Siegel as a particular case.

Authors:Yuhui Chen; Jingchi Huang Pages: 459 - 499 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Yuhui Chen, Jingchi Huang Motivated by [21], we consider the global wellposedness to the 3-D incompressible inhomogeneous Navier–Stokes equations with large horizontal velocity. In particular, we proved that when the initial density is close enough to a positive constant, then given divergence free initial velocity field of the type ( v 0 h , 0 ) ( x h ) + ( w 0 h , w 0 3 ) ( x h , x 3 ) , we shall prove the global wellposedness of (1.1). The main difficulty here lies in the fact that we will have to obtain the L 1 ( R + ; Lip ( R 3 ) ) estimate for convection velocity in the transport equation of (1.1). Toward this and due to the strong anisotropic properties of the approximate solutions, we will have to work in the framework of anisotropic Littlewood–Paley theory here.

Authors:Jacek Cyranka; Piotr Bogusław Mucha Pages: 500 - 530 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Jacek Cyranka, Piotr Bogusław Mucha The paper aims at constructing two different solutions to an elliptic system u ⋅ ∇ u + ( − Δ ) m u = λ F defined on the two dimensional torus. It can be viewed as an elliptic regularization of the stationary Burgers 2D system. A motivation to consider the above system comes from an examination of unusual properties of the linear operator λ sin y ∂ x w + ( − Δ ) m w arising from a linearization of the equation about the dominant part of F. We argue that the skew-symmetric part of the operator provides in some sense a smallness of norms of the linear operator inverse. Our analytical proof is valid for a particular force F and for λ > λ 0 , m > m 0 sufficiently large. The main steps of the proof concern finite dimension approximation of the system and concentrate on analysis of features of large matrices, which resembles standard numerical analysis. Our analytical results are illustrated by numerical simulations.

Authors:Shuaibing Luo; Kei Ji Izuchi; Rongwei Yang Pages: 531 - 546 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Shuaibing Luo, Kei Ji Izuchi, Rongwei Yang A closed subspace M of the Hardy space H 2 ( D 2 ) over the bidisk is called a submodule if it is invariant under multiplication by coordinate functions z 1 and z 2 . Whether every finitely generated submodule is Hilbert–Schmidt is an unsolved problem. This paper proves that every finitely generated submodule M containing z 1 − φ ( z 2 ) is Hilbert–Schmidt, where φ is any finite Blaschke product. Some other related topics such as fringe operator and Fredholm index are also discussed.

Authors:M. Cristina Câmara; Jonathan R. Partington Pages: 557 - 570 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): M. Cristina Câmara, Jonathan R. Partington Multipliers between kernels of Toeplitz operators are characterised in terms of test functions (so-called maximal vectors for the kernels); these maximal vectors may easily be parametrised in terms of inner and outer factorisations. Immediate applications to model spaces are derived. The case of surjective multipliers is also analysed. These ideas are applied to describing equivalences between two Toeplitz kernels.

Authors:Agnid Banerjee Pages: 571 - 587 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Agnid Banerjee Based on a variant of the frequency function approach of Almgren ([1]), under appropriate assumptions we establish an optimal upper bound on the vanishing order of solutions to stationary Schrödinger equations associated to sub-Laplacian on Carnot groups of arbitrary step. Such a bound provides a quantitative form of strong unique continuation and can be thought of as a subelliptic analogue of the recent results obtained by Bakri ([3]) and Zhu ([27]) for the standard Laplacian.

Authors:Duc Quang Si Pages: 604 - 623 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Duc Quang Si Let Q 1 , . . . , Q q be q slowly moving hypersurfaces in P n ( C ) of degree d i which are located in N-subgeneral position. Let f be a meromorphic mapping from C m into P n ( C ) which is algebraically nondegenerate over the field generated by Q i 's. In this paper, we will prove that, for every ϵ > 0 , there exists a positive integer M such that ( q − ( N − n + 1 ) ( n + 1 ) − ϵ ) T f ( r ) ≤ ∑ i = 1 q 1 d i N [ M ] ( r , f ⁎ Q i ) + o ( T f ( r ) ) . Moreover, an explicit estimate for M is given. Our result is an extension of the previous second main theorems for meromorphic mappings and moving hypersurfaces.

Authors:Yu-Long Zhang; Jun-Min Wang Pages: 643 - 657 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Yu-Long Zhang, Jun-Min Wang Using the moment approach, we consider the boundary exact controllability of an active constrained layer (ACL) beam consisting of three layers, which is modeled as a Rayleigh beam coupled with two wave equations. We convert the controllability problem of the ACL beam into a corresponding moment problem which can be solvable in a Hilbert space ℓ 2 . Then, we conclude that the ACL beam is exactly controllable when the control time is greater than the maximum value among of the optical lengths of the two waves and the square root of the moment of inertia of the Rayleigh beam. The well-posedness and asymptotic spectral expressions of the ACL beam are also presented.

Authors:Shuan Tang; Yuliang Shen Pages: 658 - 672 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Shuan Tang, Yuliang Shen This paper deals with the p-integrable Teichmüller space and gives an intrinsic characterization of a p-integrable asymptotic affine homeomorphism for p > 2 . More precisely, it is proved that a sense-preserving homeomorphism h on the unit circle is p-integrable asymptotic affine, namely, h can be extended to a quasiconformal mapping to the unit disk whose Beltrami coefficient is p-integrable in the Poincaré metric if and only if h is absolutely continuous such that log h ′ belongs to the Besov class B p ( S 1 ) .

Authors:Zafer Selcuk Aygin Pages: 690 - 702 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Zafer Selcuk Aygin We use properties of modular forms to prove the following extension of the Ramanujan–Mordell formula, z k − j z p j = p χ k − j − 1 p χ k − 1 F p ( k , j ; τ ) + p χ k − p χ k − j p χ k − 1 F p ( k , j ; p τ ) + z k A p ( k , j ; τ ) , for all 1 < k ∈ N , 0 ≤ j ≤ k and p an odd prime. We obtain this result by computing the Fourier series expansions of modular forms at all cusps of Γ 0 ( 4 p ) .

Authors:Sun-Chul Kim Pages: 703 - 711 Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Sun-Chul Kim A free-boundary problem for two-dimensional Euler flows with uniform vorticity on the surface of sphere is considered using the stereographic projection and the argument principle in complex variables. With the constant speed condition on the boundary, a circle turns out to be the unique solution on the sphere.

Authors:Zahra Afsar; Astrid an Huef; Iain Raeburn Pages: 965 - 1009 Abstract: Publication date: 15 August 2018 Source:Journal of Mathematical Analysis and Applications, Volume 464, Issue 2 Author(s): Zahra Afsar, Astrid an Huef, Iain Raeburn We consider a family of ⁎-commuting local homeomorphisms on a compact space, and build a compactly aligned product system of Hilbert bimodules. The Nica–Toeplitz algebra of this system carries a gauge action of a higher-dimensional torus, and there are many possible dynamics obtained by composing with different embeddings of the real line in this torus. We study the KMS states of these dynamics. For large inverse temperatures including ∞, we describe the simplex of KMS states on the Nica–Toeplitz algebra. We illustrate our main theorem by considering backward shifts on the infinite-path spaces of a class of k-graphs whose shift maps ⁎-commute.

Authors:Arkady Poliakovsky Pages: 1010 - 1050 Abstract: Publication date: 15 August 2018 Source:Journal of Mathematical Analysis and Applications, Volume 464, Issue 2 Author(s): Arkady Poliakovsky We introduce a new method to reformulate certain classes of problems involving non-local terms as local problems. This allows us to apply the techniques developed in [24,25] to prove upper and lower bounds for problems arising in Micromagnetics and in the variational study of the Method of Vanishing Viscosity for systems of conservation laws.

Authors:Marta Latorre; Sergio Segura de León Pages: 1051 - 1081 Abstract: Publication date: 15 August 2018 Source:Journal of Mathematical Analysis and Applications, Volume 464, Issue 2 Author(s): Marta Latorre, Sergio Segura de León This paper is concerned with an evolution problem having an elliptic equation involving the 1-Laplacian operator and a dynamical boundary condition. We apply nonlinear semigroup theory to obtain existence and uniqueness results as well as a comparison principle. Our main theorem shows that the solution we found is actually a strong solution. We also compare solutions with different data.

Authors:Xinguang Zhang; Lishan Liu; Yonghong Wu; Yujun Cui Pages: 1089 - 1106 Abstract: Publication date: 15 August 2018 Source:Journal of Mathematical Analysis and Applications, Volume 464, Issue 2 Author(s): Xinguang Zhang, Lishan Liu, Yonghong Wu, Yujun Cui In this paper, we establish some new results on the existence and nonexistence of radial large positive solutions for a modified Schrödinger system with a nonconvex diffusion term by a successive iteration technique and the dual approach. The necessary and sufficient condition for the existence of radial large positive solutions is established. Our results improve and extend many previous work in this field of research.

Authors:Hai-Hua Wu; Yue-Ping Jiang; Xin-Han Dong Pages: 1107 - 1118 Abstract: Publication date: 15 August 2018 Source:Journal of Mathematical Analysis and Applications, Volume 464, Issue 2 Author(s): Hai-Hua Wu, Yue-Ping Jiang, Xin-Han Dong For a tangential slit, the behavior of the driving function in the Loewner differential equation is less clear. In this paper, we investigate the tangential slit φ ( Γ ) , where φ is a univalent real analytic function near the origin, and where Γ is a circular arc tangent at the origin. Our main aim is to give an interesting way to prove the asymptotic property of the driving function which generates the tangential slit φ ( Γ ) .

Authors:Pandolfi Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): L. Pandolfi In this paper we solve the problem of the identification of a coefficient which appears in the equation of a distributed system with persistent memory. This system is encountered for example when modelling the interconnection of linear elastic and viscoelastic systems. The additional data used in the identification are subsumed in the input output map from the deformation to the traction on the boundary. We extend a dynamical approach to identification introduced by Belishev in the case of purely elastic (memoryless) bodies and based on a special equation due to Blagoveshchenskiı̌. So, in particular, we extend Blagoveshchenskiı̌ equation to our class of systems with persistent memory.

Authors:Ramesh Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): G. Ramesh A bounded linear operator T : H 1 → H 2 , where H 1 , H 2 are Hilbert spaces is said to be norm attaining if there exists a unit vector x ∈ H 1 such that ‖ T x ‖ = ‖ T ‖ . If for any closed subspace M of H 1 , the restriction T M : M → H 2 of T to M is norm attaining, then T is called an absolutely norm attaining operator or AN -operator. We prove the following characterization theorem: a positive operator T defined on an infinite dimensional Hilbert space H is an AN -operator if and only if the essential spectrum of T is a single point and [ m ( T ) , m e ( T ) ) contains atmost finitely many points. Here m ( T ) and m e ( T ) are the minimum modulus and essential minimum modulus of T, respectively. As a consequence we obtain a sufficient condition under which the AN -property of an operator implies AN -property of its adjoint. We also study the structure of paranormal AN -operators and give a necessary and sufficient condition under which a paranormal AN -operator is normal.

Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): M. Kandić, A. Vavpetič In this paper we find sufficient and necessary conditions under which vector lattice C ( X ) and its sublattices C b ( X ) , C 0 ( X ) and C c ( X ) have the countable sup property. It turns out that the countable sup property is tightly connected to the countable chain condition of the underlying topological space X. We also consider the countable sup property of C ( X × Y ) . Even when both C ( X ) and C ( Y ) have the countable sup property it is possible that C ( X × Y ) fails to have it. For this construction one needs to assume the continuum hypothesis. In general, we present a positive result in this direction and also address the question when C ( ∏ λ ∈ Λ X λ ) has the countable sup property. Our results can be understood as vector lattice theoretical versions of results regarding products of spaces satisfying the countable chain condition. We also present new results for general vector lattices that are of an independent interest.

Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Salomón Alarcón We study the problem (P α ) − Δ u = x α u 4 + 2 α N − 2 − ε u in Ω , u = 0 on ∂ Ω , where Ω is a bounded smooth domain in R N , N ≥ 3 , which is symmetric with respect to x 1 , x 2 , … , x N and contains the origin, α > 0 , and ε > 0 is a small parameter. We construct solutions to ( P α ) with the shape of a sign-changing tower of bubbles of order α that concentrate and blow-up at the origin as ε → 0 . We also study a slightly Hénon supercritical dual version of ( P α ) in an exterior domain, for which we found solutions with the shape of a flat sign-changing tower of bubbles of order α that disappear as ε → 0 .

Authors:Steffen Abstract: Publication date: 1 September 2018 Source:Journal of Mathematical Analysis and Applications, Volume 465, Issue 1 Author(s): Steffen Löbrich We compute the Fourier coefficients of analogues of Kohnen and Zagier's modular forms f k , Δ of weight 2 and negative discriminant. These functions can also be written as twisted traces of certain weight 2 Poincaré series with evaluations of Niebur–Poincaré series as Fourier coefficients. This allows us to study twisted traces of singular moduli in an integral weight setting. In particular, we recover explicit series expressions for twisted traces of singular moduli and extend algebraicity results by Bengoechea to the weight 2 case. We also compute regularized inner products of these functions, which in the higher weight case have been related to evaluations of higher Green's functions at CM-points.

Authors:Hongmin Abstract: Publication date: 15 August 2018 Source:Journal of Mathematical Analysis and Applications, Volume 464, Issue 2 Author(s): Hongmin Li We discuss the short-wave limit of a new three-component Degasperis–Procesi equation, and construct infinitely many conserved quantities for the degenerate system. We study the reductions for a spectral problem of the degenerate system, which are shown to contain spectral problems of some famous or new systems found recently.

Authors:Devaraj Abstract: Publication date: 15 August 2018 Source:Journal of Mathematical Analysis and Applications, Volume 464, Issue 2 Author(s): Devaraj P. Let G be a locally compact abelian group and μ be a compactly supported discrete measure on G. We analyse the range of the operator C μ : C ( G ) ⟶ C ( G ) defined by C μ ( f ) ( x ) = ( f ⋆ μ ) ( x ) = ∫ G f ( x − y ) d μ ( y ) . It is shown that this operator is onto when G is a compactly generated locally compact abelian group and μ satisfies certain compatibility conditions. Furthermore, if G is a compactly generated torsion free locally compact abelian group then the convolution operator is always onto for every non zero compactly supported discrete measure μ. For a g ∈ C ( G ) , we construct a function f ∈ C ( G ) such that f ⋆ μ = g .