Stability of global wave front sets by perturbations of frames

TL;DR

This paper demonstrates that the Gabor wave front set of ultradistributions remains stable under certain perturbations of the Gabor frame, including Christensen-type and nonstationary frames.

Contribution

It establishes the invariance of the Gabor wave front set under specific frame perturbations for ultradistributions, extending previous stability results.

Findings

Wave front set stability under Christensen-type perturbations

Stability under nonstationary Gabor frames

Applicable to ultradistributions in ultradifferentiable functions

Abstract

In this paper we consider the Gabor wave front set of ultradistributions in the frame of ultradifferentiable functions. We prove that such a wave front set, defined through a Gabor frame on a regular lattice, is not affected by perturbations of the frame, in two different cases: when we consider $\varepsilon$-perturbations of Christensen type, and when we consider nonstationary Gabor frames.