相关论文: On Riesz duals for the Gabor system on LCA groups

We extend a result proved in \cite{Col} for mirror symmetries of planar systems to measure-preserving non-linear reversibilities of $n$-dimensional systems, dropping the analyticity and nondegeneracy conditions.

We give an explicit criterion for a rational lattice in the time-frequency plane to admit a Gabor frame with window in the Schwartz class. The criterion is an inequality formulated in terms of the lattice covolume, the dimension of the…

A completeness theorem is proved involving a system of integro-differential equations with some $\lambda$-depending boundary conditions. Also some sufficient conditions for the root functions to form a Riesz basis are established.

A finite group is said to be weakly separable if every algebraic isomorphism between two $S$-rings over this group is induced by a combinatorial isomorphism. In the paper we prove that every abelian weakly separable group belongs to one of…

Following Roberts' work in the case of orthogonal-symplectic similitude dual pairs, we study the local theta correspondence for unitary similitude dual pairs over a $p$-adic field.

In this article we establish a version of Koszul duality for filtered rings arising from $p$-adic Lie groups. Our precise setup is the following. We let $G$ be a uniform pro-$p$ group and consider its completed group algebra…

In this paper we give an extension of the Barbashin-Krasovski-LaSalle Theorem to a class of time-varying dynamical systems, namely the class of systems for which the restricted vector field to the zero-set of the time derivative of the…

We present in this paper a construction for Gabor-type frames built out of generalized Weyl-Heisenberg groups. These latter are obtained via central extensions of groups which are direct products of locally compact abelian groups and their…

A Gorenstein A-algebra R of codimension 2 is a perfect finite A-algebra such that R=Ext^2(R,A) holds as R-modules, A being a Cohen-Macaulay local ring with dim(A)-dim_A(R)=2. I prove a structure theorem for these algebras improving on an…

We study a class of double coset spaces R_A \backslash G_1 \times G_2 /R_C, where G_1 and G_2 are connected reductive algebraic groups, and R_A and R_C are certain spherical subgroups of G_1 \times G_2 obtained by ``identifying'' Levi…

We emulate the Rademacher functions on any non-commutative compact group requiring the resulting system to have pairwise disjoint spectra.

The aim of this work is to study (Multi-window) Gabor systems in the space \(\ell^2(\mathbb{Z} \times \mathbb{Z}, \mathbb{H})\), denoted by $\mathcal{G}(g,L,M,N)$, and defined by: \[ \left\{ (k_1,k_2)\in \mathbb{Z}^2\mapsto e^{2\pi i…

We construct a simplified resolution for the trivial G-module Z, where G is a finite abelian group, and compare it with the standard resolution. We use it to calculate cohomologies of irreducible G-lattices and their duals.

We discuss the concepts of pseudo-dual frames and approximately dual frames, and illuminate their relationship to classical frames. Approximately dual frames are easier to construct than the classical dual frames, and might be tailored to…

The aim of these notes is to generalize Laumon's construction [18] of automorphic sheaves corresponding to local systems on a smooth, projective curve $C$ to the case of local systems with indecomposable unipotent ramification at a finite…

We study the compatibility of Arthur's conjecture for $R$-groups in the restriction of discrete series representations from Levi subgroups of a $p$-adic group to those of its closed subgroup having the same derived group. The compatibility…

For any Lie group G a renormalization map R on the space of simple G-extensions of Interval Exchange Transformations is constructed. R is applied to prove weak mixing and cohomological non-equivalence of typical G-extensions over IETs, when…

Suppose $G$ is a locally solid lattice group. It is known that there are non-equivalent classes of bounded homomorphisms on $G$ which have topological structures. In this paper, our attempt is to assign lattice structures on them. More…

Let $G$ be a connected, simply connected, nilpotent Lie group whose irreducible unitary representations are square-integrable modulo the center. We obtain characterization results for reproducing formulas associated with the left…

The Pl\"unnecke-Ruzsa inequality is a fundamental tool to control the growth of finite subsets of abelian groups under repeated addition and subtraction. Other tools to handle sumsets have gained applicability by being extended to more…