Discrete Wave-front sets of Fourier Lebesgue and modulation space types

TL;DR

This paper introduces discrete wave-front sets for Fourier Lebesgue and modulation spaces and proves their equivalence to the continuous wave-front sets, advancing the understanding of microlocal analysis in these function spaces.

Contribution

It defines discrete wave-front sets for Fourier Lebesgue and modulation spaces and establishes their equivalence with continuous wave-front sets, providing a new framework for microlocal analysis.

Findings

Discrete wave-front sets are equivalent to continuous ones in these spaces

The framework enhances microlocal analysis techniques

Provides new tools for analyzing singularities in Fourier Lebesgue and modulation spaces

Abstract

We introduce discrete wave-front sets with respect to Fourier Lebesgue and modulation spaces. We prove that these wave-front sets agree with corresponding wave-front sets of "continuous type".