# Planar sampling sets for the short-time Fourier transform

## TL;DR

This paper investigates sampling bounds for the short-time Fourier transform on planar domains, providing quantitative estimates for Hermite windows and conditions based on planar density, along with a Remez-type inequality for polyanalytic functions.

## Contribution

It introduces new sampling bounds for the short-time Fourier transform on nonzero measure domains, including a quantitative estimate for Hermite windows and a density-based sufficient condition for a broad class of windows.

## Key findings

- Quantitative lower sampling bound for Hermite windows
- Sufficient density condition for window sampling
- Remez-type inequality for polyanalytic functions

## Abstract

This paper considers the problem of restricting the short-time Fourier transform to domains of nonzero measure in the plane and studies sampling bounds of such systems. In particular, we give a quantitative estimate for the lower sampling bound in the case of Hermite windows and derive a sufficient condition for a large class of windows in terms of a certain planar density. On the way, we prove a Remez-type inequality for polyanalytic functions. MSC2010: 42C40, 46E15, 46E20, 42C15