Related papers: Sampling and interpolation in Bargmann-Fock spaces…
We prove a.s. (almost sure) unisolvency of interpolation by continuous random sampling with respect to any given density, in spaces of multivariate a.e. (almost everywhere) analytic functions. Examples are given concerning polynomial and…
We deal with the task of sampling from an unnormalized Boltzmann density $\rho_D$ by learning a Boltzmann curve given by energies $f_t$ starting in a simple density $\rho_Z$. First, we examine conditions under which Fisher-Rao flows are…
Strongly correlated systems of fermions have an interesting phase diagram arising from the Hubbard gap. Excitation across the gap leads to the formation of doubly occupied lattice sites (doublons). This state offers interesting electronic…
We derive frame estimates for vector-valued Gabor systems with window functions belonging to Schwartz space. The main result provides frame bound estimates for windows composed of Hermite functions. The proof is based on a recently…
Interpolation inequalities in Triebel-Lizorkin-Lorentz spaces and Besov-Lorentz spaces are studied for both inhomogeneous and homogeneous cases. First we establish interpolation inequalities under quite general assumptions on the parameters…
A Gabor system generated by a window function $g\in L^2(\mathbb{R}^d)$ and a separable set $\Lambda\times \Gamma \subset \mathbb{R}^{2d}$ is the collection of time-frequency shifts of $g$ given by $\mathcal G(g, \Lambda\times \Gamma) =…
The properties of the Gabor and Morlet transforms are examined with respect to the Fourier analysis of discretely sampled data. Forward and inverse transform pairs based on a fixed window with uniform sampling of the frequency axis can…
The purpose of this paper is to study the Sarason's problem on Fock spaces of polyanalytic functions. Namely, given two polyanalytic symbols $f$ and $g$, we establish a necessary and sufficient condition for the boundedness of some Toeplitz…
We study sampling and interpolation arrays with multiplicities for the spaces P_k of holomorphic polynomials of degree at most k. We find that the geometric conditions satisfied by these arrays are in accordance with the conditions…
We study the fractal uncertainty principle in the joint time-frequency representation, and we prove a version for the Short-Time Fourier transform with Gaussian window on the modulation spaces. This can equivalently be formulated in terms…
In this paper, we obtain two interpolation theorems on convex-set valued Lebesgue spaces, which generalize the Marcinkiewicz interpolation theorem and Riesz-Thorin interpolation theorem on classical Lebesgue spaces, respectively. As…
The goal of the paper is to consider Bernstein-Mellin subspaces in the Lebesgue-Mellin spaces and establishing for functions in these subspaces new sampling theorems and Riesz-Boas high-order interpolation formulas.
We consider the problem of sampling from a density of the form $p(x) \propto \exp(-f(x)- g(x))$, where $f: \mathbb{R}^d \rightarrow \mathbb{R}$ is a smooth and strongly convex function and $g: \mathbb{R}^d \rightarrow \mathbb{R}$ is a…
We prove interpolation estimates between Morrey-Campanato spaces and Sobolev spaces. These estimates give in particular concentration-compactness inequalities in the translation-invariant and in the translation- and dilation-invariant case.…
This paper deals with some special integral transforms of Bargmann-Fock type in the setting of quaternionic valued slice hyperholomorphic and Cauchy-Fueter regular functions. The construction is based on the well-known Fueter mapping…
The well know conjecture of {\it Coburn} [{\it L.A. Coburn, {On the Berezin-Toeplitz calculus}, Proc. Amer. Math. Soc. 129 (2001) 3331-3338.}] proved by {\it Lo} [{\it M-L. Lo, {The Bargmann Transform and Windowed Fourier Transform},…
In this paper, we introduce a new scale of tent spaces which covers, the (weighted) tent spaces of Coifman-Meyer-Stein and of Hofmann-Mayboroda-McIntosh, and some other tent spaces considered by Dahlberg, Kenig-Pipher and Auscher-Axelsson…
We apply a new approach to the study of the density of Gabor systems, and obtain a simple and straightforward proof of Ramanathan and Steger's well known result regarding the density of Gabor frames and Gabor Riesz sequences. Moreover, this…
We consider smoothness properties of the generator of a principal Gabor space on the real line which is invariant under some additional translation-modulation pair. We prove that if a Gabor system on a lattice with rational density is a…
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…