Related papers: Remarks on multivariate Gaussian Gabor frames
We show that a sufficient density condition for Gabor systems with Hermite functions over lattices is not sufficient in general. This follows from a result on how zeros of the Zak transform determine the frame property of integer…
We use the concept of reproducing pairs to study Gabor systems at critical density. First, we present a generalization of the Balian-Low theorem to the reproducing pairs setting. Then, we prove our main result that there exists a…
We consider Gabor frames generated by a general lattice and a window function that belongs to one of the following spaces: the Sobolev space $V_1 = H^1(\mathbb R^d)$, the weighted $L^2$-space $V_2 = L_{1 + |x|}^2(\mathbb R^d)$, and the…
We investigated the equilibrium properties of a one-dimensional system of classical particles which interact in pairs through a bounded repulsive potential with a Gaussian shape. Notwithstanding the absence of a proper fluid-solid phase…
We show that multi-window Gabor frames with windows in the Wiener algebra $W(L^{\infty}, \ell^{1})$ are Banach frames for all Wiener amalgam spaces. As a byproduct of our results we positively answer an open question that was posed by…
We give large deviation upper bounds, and discuss lower bounds, for the Gibbs-KMS state of a system of quantum spins or an interacting Fermi gas on the lattice. We cover general interactions and general observables, both in the high…
We extend the Gabor analysis in \cite{GaSa} to a broad class of modulation spaces, allowing more general mixed quasi-norm estimates and weights in the definition of the modulation space quasi-norm. For such spaces we deduce invariance and…
The glass problem is notoriously hard and controversial. Even at the mean-field level, little is agreed about how a fluid turns sluggish while exhibiting but unremarkable structural changes. It is clear, however, that the process involves…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
In this work we deal with the recently introduced concept of weaving frames. We extend the concept to include multi-window frames and present the first sufficient criteria for a family of multi-window Gabor frames to be woven. We give a…
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 present the first detailed computations of wave optics effects in the gravitational lensing of binary systems. The field is conceptually rich, combining the caustic singularities produced in classical gravitational lensing with quantum…
Gabor frames have interested many mathematicians and physicists due to their potential applications in time-frequency analysis, in particular, signal processing. A Gabor system is a collection of vectors which is obtained by applying…
Despite its mathematical complexity, the multiple gravitational lens can be studied in detail in every situation where a perturbative approach is possible. In this paper, we examine the caustics of a system with a lens very far from the…
We investigate the relation between two different mathematical problems: the construction of bounds on sphere packing density using Cohn-Elkies functions and the construction of Gabor frames for signal analysis. In particular, we present a…
We study number density distribution and the behavior of time correlation functions in the density of grains for a quasi-two dimensional system of vibrated grains. We study the system at various packing fractions, from low to high. At low…
In this article we are going to discuss the conjecture of Strohmer and Beaver for Gaussian Gabor systems. It asks for an optimal sampling pattern in the time-frequency plane, where optimality is measured in terms of the condition number of…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
We apply a recently developed measure of multiscale complexity to the Gaussian model consisting of continuous spins with bilinear interactions for a variety of interaction matrix structures. We find two universal behaviors of the complexity…
The goal of this paper is to give some rigorous results, concerning high density behavior of Fermi systems.