Related papers: Gabor frames for rational functions

The topic of this paper are (multi-window) Gabor frames for signals over finite Abelian groups, generated by an arbitrary lattice within the finite time-frequency plane. Our generic approach covers simultaneously multi-dimensional signals…

We construct a uniformly discrete sequence $\{\lambda_1 < \lambda_2 < \cdots\} \subset \mathbb{R}$ and functions $g$ and $\{g_n^*\}$ in $L^2(\mathbb{R})$, such that every $f \in L^2(\mathbb{R})$ admits a series expansion \[ f(x) =…

The duality principle for Gabor frames is one of the pillars of Gabor analysis. We establish a far-reaching generalization to Morita equivalent $C^*$-algebras where the equivalence bimodule is a finitely generated projective Hilbert…

We characterize the normal operators $A$ on $\ell^2$ and the elements $a^i \in \ell^2$, with $1\le i\le m$, such that the sequence $$\{ A^n a^1 , \ldots , A^n a^m \}_{n\ge 0}$$ is a frame. The characterization makes strong use of the…

This work developes a quantitative framework for describing the overcompleteness of a large class of frames. A previous paper introduced notions of localization and approximation between two frames $\mathcal{F} = \{f_i\}_{i \in I}$ and…

The notion of faithful flatness of a module over a commutative ring is studied for two $R$-modules $M$ arising in functional analysis, where $R$ is a Banach algebra and $M$ is a Hilbert space. The following results are shown: If $X$ is a…

This paper establishes sufficient conditions that force a graph to contain a bipartite subgraph with a given structural property. In particular, let $\beta$ be any of the following graph parameters: Hadwiger number, Haj\'{o}s number,…

We obtain Gabor frame characterisations of modulation spaces defined via a class of translation-modulation invariant Banach spaces of distributions that was recently introduced in $[10]$. We show that these spaces admit an atomic…

We study spanning properties of a family of functions translated along simple model sets. We characterize tight frame and dual frame generators for such irregular translates and we apply the results to Gabor systems. We use the connection…

We use the method of group contractions to relate wavelets analysis and Gabor analysis. Wavelets analysis is associated with unitary irreducible representations of the affine group while Gabor analysis is associated with unitary irreducible…

Let $\Gamma=\langle T_{k},M_{l}:k\in\mathbb{Z}^{d},l\in B\mathbb{Z}% ^{d}\rangle $ be a group of unitary operators where $T_{k}$ is a translation operator and $M_{l}$ is a modulation operator acting on $L^{2}\left( \mathbb{R}^{d}\right) .$…

Let $\mathfrak{g}$ be a finite or an affine type Lie algebra over $\mathbb{C}$ with root system $\Delta$. We show a parabolic generalization of the partial sum property for $\Delta$, which we term the parabolic partial sum property. It…

We prove that a Hilbert space frame $\fti$ contains a Riesz basis if every subfamily $\ftj , J \subseteq I ,$ is a frame for its closed span. Secondly we give a new characterization of Banach spaces which do not have any subspace isomorphic…

Let $F$ be an algebraically closed field of characteristic $p$. We fashion an infinite dimensional basic algebra $\underleftarrow{\mathcal{C}}_p(F)$, with a transparent combinatorial structure, which we expect to control the rational…

In this work, we analyze Gabor frames for the Weyl--Heisenberg group and wavelet frames for the extended affine group. Firstly, we give necessary and sufficient conditions for the existence of nonstationary frames of translates. Using these…

We consider algebras with basis numerated by elements of a group $G.$ We fix a function $f$ from $G\times G$ to a ground field and give a multiplication of the algebra which depends on $f$. We study the basic properties of such algebras. In…

In this paper, it is shown that the diagonal coset vertex operator algebra $C(L_{\mathfrak{g}}(k+2,0),L_{\mathfrak{g}}(k,0)\otimes L_{\mathfrak{g}}(2,0))$ is rational and $C_2$-cofinite in case $\mathfrak{g}=so(2n), n\geq 3$ and $k$ is an…

We study mirror symmetric pairs of Calabi--Yau manifolds over finite fields. In particular we compute the number of rational points of the manifolds as a function of the complex structure parameters. The data of the number of rational…

We study Lagrangian systems on a closed manifold. We link the differentiability of Mather's beta-function with the topological complexity of the complement of the Aubry set. As a consequence, when the dimension of the manifold is less than…

Let $a$, $b$ be two fixed non-zero constants. A measurable set $E\subset \mathbb{R}$ is called a Weyl-Heisenberg frame set for $(a, b)$ if the function $g=\chi_{E}$ generates a Weyl-Heisenberg frame for $L^2(\mathbb{R})$ under modulates by…