Gabor single-frame and multi-frame multipliers in any given dimension

TL;DR

This paper provides a comprehensive characterization of Gabor multipliers for single-frame and multi-frame generators across any dimension, extending previous results and offering a general approach for separable lattices.

Contribution

It introduces a complete characterization of Gabor multipliers for any dimension and separable lattices, generalizing earlier special-case results.

Findings

Characterization applies to all dimensions and separable lattices.

The approach generalizes previous specific cases.

Results facilitate understanding of Gabor multipliers in high-dimensional settings.

Abstract

Functional Gabor single-frame or multi-frame generator multipliers are the matrices of function entries that preserve Parseval Gabor single-frame or multi-frame generators. An interesting and natural question is how to characterize all such multipliers. This question has been answered for several special cases including the case of single-frame generators in two dimensions and the case of multi-frame generators in one-dimension. In this paper we completely characterize multipliers for Gabor single-frame and multi-frame generators with respect to separable time-frequency lattices in any given dimension. Our approach is general and applies to the previously known cases as well.