Authors:Ana Cristina López Martín Pages: 219 - 227 Abstract: We extend to quasi-projective schemes that kind of Bondal-Orlov’s criterion for a Fourier-Mukai functor to be fully faithful and we prove a variant of it valid in arbitrary characteristic. As a first application of these criteria we prove the fully faithfulness of the Fourier-Mukai functor used to show the autoduality of the compactified Jacobian for reduced projective curves with locally planar singularities. PubDate: 2017-05-01 DOI: 10.1007/s13348-016-0179-x Issue No:Vol. 68, No. 2 (2017)

Authors:Anders Björn; Jana Björn; Juha Lehrbäck Pages: 229 - 241 Abstract: We obtain upper and lower bounds for the nonlinear variational capacity of thin annuli in weighted \(\mathbf {R}^n\) and in metric spaces, primarily under the assumptions of an annular decay property and a Poincaré inequality. In particular, if the measure has the 1-annular decay property at \(x_0\) and the metric space supports a pointwise 1-Poincaré inequality at \(x_0\) , then the upper and lower bounds are comparable and we get a two-sided estimate for thin annuli centred at \(x_0\) . This generalizes the known estimate for the usual variational capacity in unweighted \(\mathbf {R}^n\) . We also characterize the 1-annular decay property and provide examples which illustrate the sharpness of our results. PubDate: 2017-05-01 DOI: 10.1007/s13348-016-0178-y Issue No:Vol. 68, No. 2 (2017)

Authors:Lars Winther Christensen; Srikanth B. Iyengar Pages: 243 - 250 Abstract: It is proved that a module M over a commutative noetherian ring R is injective if \(\mathrm {Ext}_{R}^{i}((R/{\mathfrak p})_{\mathfrak p},M)=0\) holds for every \(i\geqslant 1\) and every prime ideal \(\mathfrak {p}\) in R. This leads to the following characterization of injective modules: If F is faithfully flat, then a module M such that \({\text {Hom}}_R(F,M)\) is injective and \({\text {Ext}}^i_R(F,M)=0\) for all \(i\geqslant 1\) is injective. A limited version of this characterization is also proved for certain non-noetherian rings. PubDate: 2017-05-01 DOI: 10.1007/s13348-016-0176-0 Issue No:Vol. 68, No. 2 (2017)

Authors:A. Baranov; Y. Belov; A. Poltoratski Pages: 251 - 263 Abstract: We characterize the Hermite–Biehler (de Branges) functions E which correspond to Schroedinger operators with \(L^2\) potential on the finite interval. From this characterization one can easily deduce a recent theorem by Horvath. We also obtain a result about location of resonances. PubDate: 2017-05-01 DOI: 10.1007/s13348-016-0168-0 Issue No:Vol. 68, No. 2 (2017)

Authors:Yu-Xia Liang; Lei Xia Pages: 265 - 278 Abstract: Given a locally compact group G, the disjoint supercyclicity of finite weighted translations with the same translation part generated by an aperiodic element acting on \(L^p(G)\) , \(1\le p<\infty \) , was investigated. PubDate: 2017-05-01 DOI: 10.1007/s13348-016-0164-4 Issue No:Vol. 68, No. 2 (2017)

Authors:Daniel Vera Pages: 279 - 299 Abstract: Shearlets on the cone are a multi-scale and multi-directional discrete system that have near-optimal representation of the so-called cartoon-like functions. They form Parseval frames, have better geometrical sensitivity than traditional wavelets and an implementable framework. Recently, it has been proved that some smoothness spaces can be associated to discrete systems of shearlets. Moreover, there exist embeddings between the classical isotropic dyadic spaces and the shearlet generated spaces. We prove boundedness of pseudo-differential operators (PDO’s) with non regular symbols on the shear anisotropic inhomogeneous Besov spaces and on the shear anisotropic inhomogeneous Triebel–Lizorkin spaces (which are up to now the only Triebel–Lizorkin-type spaces generated by either shearlets or curvelets and more generally by any parabolic molecule, as far as we know). The type of PDO’s that we study includes the classical Hörmander definition with x-dependent parameter \(\delta \) for a range limited by the anisotropy associated to the class. One of the advantages is that the anisotropy of the shearlet spaces is not adapted to that of the PDO. PubDate: 2017-05-01 DOI: 10.1007/s13348-016-0167-1 Issue No:Vol. 68, No. 2 (2017)

Authors:Paul Hagelstein; Ioannis Parissis; Olli Saari Abstract: Let \(A_\infty ^+\) denote the class of one-sided Muckenhoupt weights, namely all the weights w for which \(\mathsf {M}^+:L^p(w)\rightarrow L^{p,\infty }(w)\) for some \(p>1\) , where \(\mathsf {M}^+\) is the forward Hardy–Littlewood maximal operator. We show that \(w\in A_\infty ^+\) if and only if there exist numerical constants \(\gamma \in (0,1)\) and \(c>0\) such that $$\begin{aligned} w(\{x \in \mathbb {R} : \, \mathsf {M}^+ \mathbf 1 _E (x)>\gamma \})\le cw(E) \end{aligned}$$ for all measurable sets \(E\subset \mathbb R\) . Furthermore, letting $$\begin{aligned} \mathsf {C_w ^+}(\alpha ){:}{=}\sup _{0<w(E)<+\infty } \frac{1}{w(E)} w(\{x\in \mathbb R:\,\mathsf {M}^+ \mathbf 1 _E(x)>\alpha \}) \end{aligned}$$ we show that for all \(w\in A_\infty ^+\) we have the asymptotic estimate \(\mathsf {C_w ^+}(\alpha )-1\lesssim (1-\alpha )^\frac{1}{c[w]_{A_\infty ^+}}\) for \(\alpha \) sufficiently close to 1 and \(c>0\) a numerical constant, and that this estimate is best possible. We also show that the reverse Hölder inequality for one-sided Muckenhoupt weights, previously proved by Martín-Reyes and de la Torre, is sharp, thus providing a quantitative equivalent definition of \(A_\infty ^+\) . Our methods also allow us to show that a weight \(w\in A_\infty ^+\) satisfies \(w\in A_p ^+\) for all \(p>e^{c[w]_{A_\infty ^+}}\) . PubDate: 2017-06-17 DOI: 10.1007/s13348-017-0201-y

Authors:C. Bocci; G. Calussi; G. Fatabbi; A. Lorenzini Abstract: In this paper we address the Hadamard product of not necessarily generic linear varieties, looking in particular at its Hilbert function. We find that the Hilbert function of the Hadamard product \(X\star Y\) of two varieties, with \(\dim (X), \dim (Y)\le 1\) , is the product of the Hilbert functions of the original varieties X and Y. Moreover, the same result is obtained for generic linear varieties X and Y as a consequence of our showing that their Hadamard product is projectively equivalent to a Segre embedding. PubDate: 2017-06-15 DOI: 10.1007/s13348-017-0200-z

Authors:Renu Chaudhary; Dwijendra N. Pandey Abstract: In this paper, we study a stochastic fractional integro-differential equation with impulsive effects in separable Hilbert space. Using a finite dimensional subspace, semigroup theory of linear operators and stochastic version of the well-known Banach fixed point theorem is applied to show the existence and uniqueness of an approximate solution. Next, these approximate solutions are shown to form a Cauchy sequence with respect to an appropriate norm, and the limit of this sequence is then a solution of the original problem. Moreover, the convergence of Faedo–Galerkin approximation of solution is shown. In the last, we have given an example to illustrate the applications of the abstract results. PubDate: 2017-05-20 DOI: 10.1007/s13348-017-0199-1

Authors:Sonia Brivio Abstract: Let E be a stable vector bundle of rank r and slope \(2g-1\) on a smooth irreducible complex projective curve C of genus \(g \ge 3\) . In this paper we show a relation between theta divisor \(\Theta _E\) and the geometry of the tautological model \(P_E\) of E. In particular, we prove that for \(r > g-1\) , if C is a Petri curve and E is general in its moduli space then \(\Theta _E\) defines an irreducible component of the variety parametrizing \((g-2)\) -linear spaces which are g-secant to the tautological model \(P_E\) . Conversely, for a stable, \((g-2)\) -very ample vector bundle E, the existence of an irreducible non special component of dimension \(g-1\) of the above variety implies that E admits theta divisor. PubDate: 2017-05-16 DOI: 10.1007/s13348-017-0198-2

Authors:Abtin Daghighi Abstract: Let \({\varOmega }\subset \mathbb {C}\) be a domain and let \(f(z)=a(z)+\bar{z}b(z),\) where a, b are holomorphic for \(z\in {\varOmega }.\) Denote by \({\varLambda }\) the set of points in \({\varOmega }\) at which \(\left f\right \) attains weak local maximum and denote by \({\varSigma }\) the set of points in \({\varOmega }\) at which \(\left f\right \) attains strict local maximum. We prove that for each \(p\in {\varLambda }\setminus {\varSigma }\) , $$\begin{aligned} \left b(p)\right =\left \left( \frac{\partial a}{\partial z} +\bar{z}\frac{\partial b}{\partial z}\right) (p)\right \end{aligned}$$ Furthermore, if there is a real analytic curve \(\kappa :I\rightarrow {\varLambda }\setminus {\varSigma }\) (where I is an open real interval), if a, b are complex polynomials, and if \(f\circ \kappa \) has a complex polynomial extension, then either f is constant or \(\kappa \) has constant curvature. PubDate: 2017-04-18 DOI: 10.1007/s13348-017-0197-3

Authors:Paolo Mantero; Jason McCullough Abstract: Let S be a polynomial ring over an algebraically closed field k. Let x and y denote linearly independent linear forms in S so that \({\mathfrak {p}}= (x,y)\) is a height two prime ideal. This paper concerns the structure of \({\mathfrak {p}}\) -primary ideals in S. Huneke, Seceleanu, and the authors showed that for \(e \ge 3\) , there are infinitely many pairwise non-isomorphic \({\mathfrak {p}}\) -primary ideals of multiplicity e. However, we show that for \(e \le 4\) there is a finite characterization of the linear, quadric and cubic generators of all such \({\mathfrak {p}}\) -primary ideals. We apply our results to improve bounds on the projective dimension of ideals generated by three cubic forms. PubDate: 2017-04-03 DOI: 10.1007/s13348-017-0196-4

Authors:José Ángel Peláez; Daniel Seco Abstract: Let \(\mathcal {D}_v\) denote the Dirichlet type space in the unit disc induced by a radial weight v for which \(\widehat{v}(r)=\int _r^1 v(s)\,\text {d}s\) satisfies the doubling property \(\int _r^1 v(s)\,\text {d}s\le C \int _{\frac{1+r}{2}}^1 v(s)\,\text {d}s.\) In this paper, we characterize the Schatten classes \(S_p(\mathcal {D}_v)\) of the generalized Hilbert operators $$\begin{aligned} \mathcal {H}_g(f)(z)=\int _0^1f(t)g'(tz)\,\text {d}t \end{aligned}$$ acting on \(\mathcal {D}_v\) , where v satisfies certain Muckenhoupt type conditions. For \(p\ge 1\) , it is proved that \(\mathcal {H}_{g}\in S_p(\mathcal {D}_v)\) if and only if $$\begin{aligned} \int _0^1 \left( (1-r)\int _{-\pi }^\pi g'(r\text {e}^{i\theta }) ^2\,\text {d}\theta \right) ^{\frac{p}{2}}\frac{{\text {d}}r}{1-r} <\infty . \end{aligned}$$ . PubDate: 2017-03-21 DOI: 10.1007/s13348-017-0195-5

Authors:J. J. Nuño-Ballesteros; B. Oréfice-Okamoto; J. N. Tomazella Abstract: Let (X, 0) be an ICIS of dimension 2 and let \(f:(X,0)\rightarrow (\mathbb C^2,0)\) be a map germ with an isolated instability. We look at the invariants that appear when \(X_s\) is a smoothing of (X, 0) and \(f_s:X_s\rightarrow B_\epsilon \) is a stabilization of f. We find relations between these invariants and also give necessary and sufficient conditions for a 1-parameter family to be Whitney equisingular. As an application, we show that a family \((X_t,0)\) is Zariski equisingular if and only if it is Whitney equisingular and the numbers of cusps and double folds of a generic linear projection are constant with respect to t. PubDate: 2017-03-20 DOI: 10.1007/s13348-017-0194-6

Authors:Shohei Nakamura; Yoshihiro Sawano Abstract: In this paper, we give necessary conditions and sufficient conditions respectively for the boundedness of the singular integral operator on the weighted Morrey spaces. We observe the phenomenon unique to the case of Morrey spaces; the \(A_q\) -theory by Muckenhoupt and Wheeden does not suffice. We also discuss the boundedness of the commutators. The difference between the maximal operator and the singular integral operators will be clarified. Further, the property of the sharp maximal operator is investigated. PubDate: 2017-02-23 DOI: 10.1007/s13348-017-0193-7

Authors:Serge Nicaise Abstract: We perform some hierarchical analyses of dissipative systems. For that purpose, we first propose a general abstract setting, prove a convergence result and discuss some stability properties. This abstract setting is then illustrated by significant examples of damped (acoustic) wave equations for which we characterize the family of reduced problems. For each concrete problems the decay of the energy is discussed and the density assumption is proved. PubDate: 2017-02-08 DOI: 10.1007/s13348-017-0192-8

Authors:Alessandra Bernardi; Joachim Jelisiejew; Pedro Macias Marques; Kristian Ranestad Abstract: Using Macaulay’s correspondence we study the family of Artinian Gorenstein local algebras with fixed symmetric Hilbert function decomposition. As an application we give a new lower bound for the dimension of cactus varieties of the third Veronese embedding. We discuss the case of cubic surfaces, where interesting phenomena occur. PubDate: 2017-01-11 DOI: 10.1007/s13348-016-0190-2

Authors:Hara Charalambous; Apostolos Thoma; Marius Vladoiu Abstract: Let \(L\subset \mathbb {Z}^n\) be a lattice and \(I_L=\langle x^{\mathbf {u}}-x^{\mathbf {v}}:\ {\mathbf {u}}-{\mathbf {v}}\in L\rangle \) be the corresponding lattice ideal in \(\Bbbk [x_1,\ldots , x_n]\) , where \(\Bbbk \) is a field. In this paper we describe minimal binomial generating sets of \(I_L\) and their invariants. We use as a main tool a graph construction on equivalence classes of fibers of \(I_L\) . As one application of the theory developed we characterize binomial complete intersection lattice ideals, a longstanding open problem in the case of non-positive lattices. PubDate: 2017-01-10 DOI: 10.1007/s13348-017-0191-9

Authors:A. Bravo; S. Encinas; B. Pascual-Escudero Abstract: The Nash multiplicity sequence was defined by Lejeune-Jalabert as a non-increasing sequence of integers attached to a germ of a curve inside a germ of a hypersurface. Hickel generalized this notion and described a sequence of blow ups which allows us to compute it and study its behavior. In this paper, we show how this sequence can be used to compute some invariants that appear in algorithmic resolution of singularities. Moreover, this indicates that these invariants from constructive resolution are intrinsic to the variety since they can be read in terms of its space of arcs. This result is a first step connecting explicitly arc spaces and algorithmic resolution of singularities. PubDate: 2017-01-04 DOI: 10.1007/s13348-016-0188-9

Authors:Ganga Ram Gautam; Jaydev Dabas Abstract: In this research article, we establish the existence results of mild solutions for semi-linear impulsive neutral fractional order integro-differential equations with state dependent delay subject to nonlocal initial condition by applying well known classical fixed point theorems. At last, we present an example of partial derivative to illuminate the results. PubDate: 2017-01-03 DOI: 10.1007/s13348-016-0189-8