Related papers: Sampling and interpolation in Bargmann-Fock spaces…
We give a criterion for higher-dimensional Gaussian Gabor frames, which is a reformulation of one of the main results in in a previous article by the first and last authors in more explicit terms. We use this formulation in order to extend…
We obtain sampling and interpolation theorems in radial weighted spaces of analytic functions for weights of arbitrary (more rapid than polynomial) growth. We give an application to invariant subspaces of arbitrary index in large weighted…
We study the problem of sampling with derivatives in shift-invariant spaces generated by totally-positive functions of Gaussian type or by the hyperbolic secant. We provide sharp conditions in terms of weighted Beurling densities. As a…
We study Gabor frames in the case when the window function is of hyperbolic secant type, i.e., $g(x) = (e^{ax}+e^{-bx})^{-1}$, ${\rm Re}\,a, {\rm Re}\,b>0$. A criterion for half-irregular sampling is obtained: for a separated…
We investigate the completeness of Gabor systems with respect to several classes of window functions on rational lattices. Our main results show that the time-frequency shifts of every finite linear combination of Hermite functions with…
We present sufficient conditions on a smooth uniformly flat hypersurface W in the unit ball to be an interpolation hypersurface or a sampling hypersurface for generalized Bergman spaces associated to the unit ball with its Bergman metric.…
We obtain estimates for the $L^{p}$-norm of the short-time Fourier transform (STFT) for functions in modulation spaces, providing information about the concentration on a given subset of $\mathbb{R}^{2}$, leading to deterministic guarantees…
It is well known that the Gabor expansions converge to identity operator in weak* sense on the Wiener amalgam spaces as sampling density tends to infinity. In this paper we prove the convergence of Gabor expansions to identity operator in…
We derive necessary density conditions for sampling and for interpolation in general reproducing kernel Hilbert spaces satisfying some natural conditions on the geometry of the space and the reproducing kernel. If the volume of shells is…
The de Branges spaces of entire functions generalise the classical Paley-Wiener space of square summable bandlimited functions. Specifically, the square norm is computed on the real line with respect to weights given by the values of…
We study multiple sampling, interpolation and uniqueness for the classical Fock spaces in the case of unbounded multiplicities. We show that there are no sequences which are simultaneously sampling and interpolating when the multiplicities…
In this work we derive a simple argument which shows that Gabor systems consisting of odd functions of $d$ variables and symplectic lattices of density $2^d$ cannot constitute a Gabor frame. In the 1--dimensional, separable case, this is a…
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 Gabor frames with Hermite window functions. Gr\"ochenig and Lyubarskii provided a sufficient density condition for their frame sets, which leads to what we call the "safety region". For rectangular lattices and Hermite windows of…
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 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 prove several results related to a Logvinenko-Sereda type theorem on dominating sets for generalized doubling Fock spaces. In particular, we give a precise polynomial dependence of the sampling constant on the relative density parameter…
This survey offers a systematic and streamlined exposition of the most important characterizations of Gabor frames over a lattice. The goal is to collect the most important characterizations of Gabor frames and offer a systematic exposition…
We develop sub-Nyquist sampling systems for analog signals comprised of several, possibly overlapping, finite duration pulses with unknown shapes and time positions. Efficient sampling schemes when either the pulse shape or the locations of…
We consider Gabor Riesz sequences generated by a lattice $\Lambda \subset \mathbb{R}^2$ and a window function $g \in L^2(\mathbb{R})$ which is well localized in both time and frequency. When $g$ belongs to the Feichtinger algebra, we prove…