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Publisher: Springer-Verlag (Total: 2351 journals)

 Archiv der Mathematik   [SJR: 0.597]   [H-I: 29]   [1 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 1420-8938 - ISSN (Online) 0003-889X    Published by Springer-Verlag  [2351 journals]
• On the number of invariant Hall subgroups under coprime action
• Authors: Haoran Yu
Pages: 201 - 204
Abstract: In this note, we not only simplify, but also generalize a recent result of Beltrán and Shao (J. Algebra 490:380–389, 2017).
PubDate: 2018-03-01
DOI: 10.1007/s00013-017-1135-z
Issue No: Vol. 110, No. 3 (2018)

• Lifting endo- p -permutation modules
• Authors: Caroline Lassueur; Jacques Thévenaz
Pages: 205 - 212
Abstract: We prove that all endo-p-permutation modules for a finite group are liftable from characteristic $$p>0$$ to characteristic 0.
PubDate: 2018-03-01
DOI: 10.1007/s00013-017-1115-3
Issue No: Vol. 110, No. 3 (2018)

• Subforms of norm forms of octonion fields
• Authors: Norbert Knarr; Markus J. Stroppel
Pages: 213 - 224
Abstract: We characterize the forms that occur as restrictions of norm forms of octonion fields. The results are applied to forms of types E $$_6$$ , E $$_7$$ , and E $$_8$$ and to positive definite forms over fields that allow a unique non-split octonion algebra, e.g., the field of rational numbers.
PubDate: 2018-03-01
DOI: 10.1007/s00013-017-1129-x
Issue No: Vol. 110, No. 3 (2018)

• Shifted convolution L -series values for elliptic curves
• Authors: Asra Ali; Nitya Mani
Pages: 225 - 244
Abstract: Using explicit constructions of the Weierstrass mock modular form and Eisenstein series coefficients, we obtain closed formulas for the generating functions of values of shifted convolution L-functions associated to certain elliptic curves. These identities provide a surprising relation between weight 2 newforms and shifted convolution L-values when the underlying elliptic curve has modular degree 1 with conductor N such that $$\text {genus}(X_0(N)) = 1$$ .
PubDate: 2018-03-01
DOI: 10.1007/s00013-017-1112-6
Issue No: Vol. 110, No. 3 (2018)

• Stability of secant bundles on the second symmetric power of curves
• Authors: Suratno Basu; Krishanu Dan
Pages: 245 - 249
Abstract: Given a rank r stable bundle over a smooth irreducible projective curve C,  there is an associated rank 2r bundle over $$S^2(C),$$ the second symmetric power of C. In this article we study the slope (semi-)stability of this bundle.
PubDate: 2018-01-19
DOI: 10.1007/s00013-018-1149-1
Issue No: Vol. 110, No. 3 (2018)

• A note on roots and powers of partial isometries
• Authors: H. Ezzahraoui; M. Mbekhta; A. Salhi; E. H. Zerouali
Pages: 251 - 259
Abstract: Let T be a bounded operator and let $$k \ge 2$$ be an integer. We study in this paper the following question: T is a partial isometry implies that $$T^k$$ is a partial isometry and conversely.
PubDate: 2018-03-01
DOI: 10.1007/s00013-017-1116-2
Issue No: Vol. 110, No. 3 (2018)

• A toy Neumann analogue of the nodal line conjecture
• Authors: J. B. Kennedy
Pages: 261 - 271
Abstract: We introduce an analogue of Payne’s nodal line conjecture, which asserts that the nodal (zero) set of any eigenfunction associated with the second eigenvalue of the Dirichlet Laplacian on a bounded planar domain should reach the boundary of the domain. The assertion here is that any eigenfunction associated with the first nontrivial eigenvalue of the Neumann Laplacian on a domain $$\Omega$$ with rotational symmetry of order two (i.e. $$x\in \Omega$$ iff $$-x\in \Omega$$ ) “should normally” be rotationally antisymmetric. We give both positive and negative results which highlight the heuristic similarity of this assertion to the nodal line conjecture, while demonstrating that the extra structure of the problem makes it easier to obtain stronger statements: it is true for all simply connected planar domains, while there is a counterexample domain homeomorphic to a disk with two holes.
PubDate: 2018-03-01
DOI: 10.1007/s00013-017-1117-1
Issue No: Vol. 110, No. 3 (2018)

• A commuting-vector-field approach to some dispersive estimates
• Authors: Willie Wai Yeung Wong
Pages: 273 - 289
Abstract: We prove the pointwise decay of solutions to three linear equations: (1) the transport equation in phase space generalizing the classical Vlasov equation, (2) the linear Schrödinger equation, (3) the Airy (linear KdV) equation. The usual proofs use explicit representation formulae, and either obtain $$L^1$$ — $$L^\infty$$ decay through directly estimating the fundamental solution in physical space or by studying oscillatory integrals coming from the representation in Fourier space. Our proof instead combines “vector field” commutators that capture the inherent symmetries of the relevant equations with conservation laws for mass and energy to get space–time weighted energy estimates. Combined with a simple version of Sobolev’s inequality this gives pointwise decay as desired. In the case of the Vlasov and Schrödinger equations, we can recover sharp pointwise decay; in the Schrödinger case we also show how to obtain local energy decay as well as Strichartz-type estimates. For the Airy equation we obtain a local energy decay that is almost sharp from the scaling point of view, but nonetheless misses the classical estimates by a gap. This work is inspired by the work of Klainerman on $$L^2$$ — $$L^\infty$$ decay of wave equations, as well as the recent work of Fajman, Joudioux, and Smulevici on decay of mass distributions for the relativistic Vlasov equation.
PubDate: 2018-03-01
DOI: 10.1007/s00013-017-1114-4
Issue No: Vol. 110, No. 3 (2018)

• Lower order eigenvalues of a system of equations of the drifting Laplacian
on the metric measure spaces
• Authors: He-Jun Sun
Pages: 291 - 303
Abstract: Let $$\Omega$$ be a bounded domain with smooth boundary in an n-dimensional metric measure space $$(\mathbb {R}^n, \langle ,\rangle , e^{-\phi }dv)$$ and let $$\mathbf {u}=(u^1, \ldots , u^n)$$ be a vector-valued function from $$\Omega$$ to $$\mathbb {R}^n$$ . In this paper, we investigate the Dirichlet eigenvalue problem of a system of equations of the drifting Laplacian: $$\mathbb {L}_{\phi } \mathbf {u} + \alpha [ \nabla (\mathrm {div}\mathbf { u}) -\nabla \phi \mathrm {div} \mathbf {u}]= - \widetilde{\sigma } \mathbf {u}$$ , in $$\Omega$$ , and $$u _{\partial \Omega }=0,$$ where $$\mathbb {L}_{\phi } = \Delta - \nabla \phi \cdot \nabla$$ is the drifting Laplacian and $$\alpha$$ is a nonnegative constant. We establish some universal inequalities for lower order eigenvalues of this problem on the metric measure space $$(\mathbb {R}^n, \langle ,\rangle , e^{-\phi }dv)$$ and the Gaussian shrinking soliton $$(\mathbb {R}^n, \langle ,\rangle _{\mathrm {can}}, e^{-\frac{ x ^2}{4}}dv, \frac{1}{2})$$ . Moreover, we give an estimate for the upper bound of the second eigenvalue of this problem in terms of its first eigenvalue on the gradient product Ricci soliton $$(\Sigma \times \mathbb {R}, \langle ,\rangle , e^{-\frac{\kappa t^2}{2}}dv, \kappa )$$ , where $$\Sigma$$ is an Einstein manifold with constant Ricci curvature $$\kappa$$ .
PubDate: 2018-01-19
DOI: 10.1007/s00013-017-1131-3
Issue No: Vol. 110, No. 3 (2018)

• On the connectedness of the set of Riemann surfaces with real moduli
• Authors: Antonio F. Costa; Rubén A. Hidalgo
Pages: 305 - 310
Abstract: The moduli space $${\mathcal {M}}_{g}$$ , of genus $$g\ge 2$$ closed Riemann surfaces, is a complex orbifold of dimension $$3(g-1)$$ which carries a natural real structure, i.e. it admits an anti-holomorphic involution $$\sigma$$ . The involution $$\sigma$$ maps each point corresponding to a Riemann surface S to its complex conjugate $$\overline{S}$$ . The fixed point set of $$\sigma$$ consists of the isomorphism classes of closed Riemann surfaces admitting an anticonformal automorphism. Inside $$\mathrm {Fix}(\sigma )$$ is the locus $${\mathcal {M}}_{g}(\mathbb {R})$$ , the set of real Riemann surfaces, which is known to be connected by results due to P. Buser, M. Seppälä, and R. Silhol. The complement $$\mathrm {Fix}(\sigma )-{\mathcal {M}}_{g}(\mathbb {R})$$ consists of the so called pseudo-real Riemann surfaces, which is known to be non-connected. In this short note we provide a simple argument to observe that $$\mathrm {Fix}(\sigma )$$ is connected.
PubDate: 2018-03-01
DOI: 10.1007/s00013-017-1132-2
Issue No: Vol. 110, No. 3 (2018)

• Convergence of powers of composition operators on certain spaces of
holomorphic functions defined on the right half plane
• Authors: M. Kumar; S. Srivastava
Abstract: This paper studies the asymptotic behaviour of the powers $$C_\varphi ^n$$ of a composition operator $$C_\varphi$$ on certain spaces of holomorphic functions defined on the right half plane $$\mathbb {C}_+$$ . It is shown that for composition operators on the Hardy spaces and the standard weighted Bergman spaces, if the inducing map $$\varphi$$ is not of parabolic type, then either the powers $$C_\varphi ^n$$ converge uniformly only to 0 or they do not converge even strongly.
PubDate: 2018-02-14
DOI: 10.1007/s00013-018-1159-z

• Carter subgroups and Fitting heights of finite groups
• Authors: Wenbin Guo; E. P. Vdovin
Abstract: Let G be a finite group possessing a Carter subgroup K. Denote by $$\mathbf {h}(G)$$ the Fitting height of G, by $$\mathbf {h}^*(G)$$ the generalized Fitting height of G, and by $$\ell (K)$$ the number of composition factors of K, that is, the number of prime divisors of the order of K with multiplicities. In 1969, E. C. Dade proved that if G is solvable, then $$\mathbf {h}(G)$$ is bounded in terms of $$\ell (K)$$ . In this paper, we show that $$\mathbf {h}^*(G)$$ is bounded in terms of $$\ell (K)$$ as well.
PubDate: 2018-02-13
DOI: 10.1007/s00013-017-1143-z

• A quantified Tauberian theorem for the Laplace-Stieltjes transform
• Authors: Markus Hartlapp
Abstract: We prove a quantified Tauberian theorem involving the Laplace-Stieltjes transform which is motivated by the work of Ingham and Karamata. For this, we consider functions which are locally of bounded variation and, therefore, get a generalisation of some results of Batty and Duyckaerts. We show that our theorem can be applied to special Dirichlet series.
PubDate: 2018-02-13
DOI: 10.1007/s00013-018-1164-2

• Isotropic functions revisited
• Authors: Julian Scheuer
Abstract: To a real n-dimensional vector space V and a smooth, symmetric function f defined on the n-dimensional Euclidean space we assign an associated operator function F defined on linear transformations of V. F shall have the property that, for each inner product g on V, its restriction $$F_{g}$$ to the subspace of g-selfadjoint operators is the isotropic function associated to f. This means that it acts on these operators via f acting on their eigenvalues. We generalize some well-known relations between the derivatives of f and each $$F_{g}$$ to relations between f and F, while also providing new elementary proofs of the known results. By means of an example we show that well-known regularity properties of $$F_{g}$$ do not carry over to F.
PubDate: 2018-02-13
DOI: 10.1007/s00013-018-1162-4

• On the $${{\varvec{p}}}$$ p -length of the mutually permutable product of
two $${{\varvec{p}}}$$ p -soluble groups
• Authors: John Cossey; Yangming Li
Abstract: Let a finite group $$G=AB$$ be the mutually permutable product of two p-soluble subgroups A and B for some prime p. We give a bound of the p-length of G from the p-lengths of A and B.
PubDate: 2018-02-10
DOI: 10.1007/s00013-018-1150-8

• Inequalities for the inverses of the polygamma functions
• Authors: Necdet Batir
Abstract: We provide an elementary proof of the left-hand side of the following inequality and give a new upper bound for it. \begin{aligned} \bigg [\frac{n!}{x-(x^{-1/n}+\alpha )^{-n}}\bigg ]^{\frac{1}{n+1}}&<((-1)^{n-1}\psi ^{(n)})^{-1}(x) \\&<\bigg [\frac{n!}{x-(x^{-1/n}+\beta )^{-n}}\bigg ]^{\frac{1}{n+1}}, \end{aligned} where $$\alpha =[(n-1)!]^{-1/n}$$ and $$\beta =[n!\zeta (n+1)]^{-1/n}$$ , which was proved in Batir (J Math Anal Appl 328:452–465, 2007), and we prove the following inequalities for the inverse of the digamma function $$\psi$$ . \begin{aligned} \frac{1}{\log (1+e^{-x})}<\psi ^{-1}(x)< e^{x}+\frac{1}{2}, \quad x\in \mathbb {R}. \end{aligned} The proofs are based on nice applications of the mean value theorem for differentiation and elementary properties of the polygamma functions.
PubDate: 2018-02-09
DOI: 10.1007/s00013-018-1156-2

• The lattices of invariant subspaces of a class of operators on the Hardy
space
• Authors: Željko Čučković; Bhupendra Paudyal
Abstract: In the authors’ first paper, a Beurling-Rudin-Korenbljum type characterization of the closed ideals in a certain algebra of holomorphic functions was used to describe the lattice of invariant subspaces of the shift plus a complex Volterra operator. The current work is an extension of the previous work and it describes the lattice of invariant subspaces of the shift plus a positive integer multiple of the complex Volterra operator on the Hardy space. Our work was motivated by a paper by Ong who studied the real version of the same operator.
PubDate: 2018-02-08
DOI: 10.1007/s00013-017-1142-0

• A volume decreasing theorem for $$\mathbf{V}$$ V -harmonic maps and
applications
• Authors: Guangwen Zhao
Abstract: We establish a volume decreasing result for V-harmonic maps between Riemannian manifolds. We apply this result to obtain corresponding results for Weyl harmonic maps from conformal Weyl manifolds to Riemannian manifolds. We also obtain corresponding results for holomorphic maps from almost Hermitian manifolds to quasi-Kähler manifolds, which generalize or improve the partial results in Goldberg and Har’El (Bull Soc Math Grèce 18(1):141–148, 1977, J Differ Geom 14(1):67–80, 1979).
PubDate: 2018-02-08
DOI: 10.1007/s00013-018-1160-6

• On the non-smoothness of the vector fields for the dynamically invariant
Beltrami coefficients
• Authors: Shengjin Huo; Hui Guo
Abstract: For $$\mu \in L^{\infty }(\Delta )$$ , the vector fields on the unit circle determined by $$\mu$$ play an important role in the theory of the universal Teichmüller space. The aim of this paper is to give some characterizations of the vector fields induced by dynamically invariant $$\mu$$ . We show that those vector fields are not contained in the Sobolev class $$H^{3/2}$$ . At last, we give some results on dynamically invariant vectors to show that the vector fields, the quasi-symmetric homeomorphisms, and the quasi-circles are closely related.
PubDate: 2018-02-08
DOI: 10.1007/s00013-018-1151-7

• Another proof of Grothendieck’s theorem on the splitting of vector
bundles on the projective line
• Authors: Claudia Schoemann; Stefan Wiedmann
Abstract: This note contains another proof of Grothendieck‘s theorem on the splitting of vector bundles on the projective line over a field k. Actually the proof is formulated entirely in the classical terms of a lattice $$\Lambda \cong k[T]^d$$ , discretely embedded into the vector space $$V \cong K_\infty ^d$$ , where $$K_\infty \cong k((1/T))$$ is the completion of the field of rational functions k(T) at the place $$\infty$$ with the usual valuation.
PubDate: 2018-02-08
DOI: 10.1007/s00013-018-1158-0

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