Marcinkiewicz-Zygmund Inequalities for Polynomials in Fock Space

TL;DR

This paper explores the connections between Marcinkiewicz-Zygmund inequalities, sampling theorems, and interpolation in Fock space, leading to a characterization of signal subspaces via Gabor frames.

Contribution

It establishes new relationships between inequalities, sampling, and interpolation in Fock space, and describes signal subspaces using Hermite functions and Gabor frames.

Findings

Characterizes Marcinkiewicz-Zygmund families in weighted L^2 spaces.

Links sampling theorems for entire functions in Fock space.

Describes signal subspaces spanned by Hermite functions with Gabor frames.

Abstract

We study the relation between Marcinkiewicz-Zygmund families for polynomials in a weighted $L^2$-space and sampling theorems for entire functions in the Fock space and the dual relation between uniform interpolating families for polynomials and interpolating sequences. As a consequence we obtain a description of signal subspaces spanned by Hermite functions by means of Gabor frames.