Gabor wave packets and evolution operators

TL;DR

This paper analyzes evolution equations with constant coefficients using Gabor analysis, revealing that their propagators have sparse Gabor matrices with exponential off-diagonal decay, applicable to various types of equations.

Contribution

It demonstrates that propagators for a broad class of evolution equations exhibit sparse Gabor matrices with exponential decay, extending Gabor analysis to hyperbolic, weakly hyperbolic, and parabolic equations.

Findings

Propagators have sparse Gabor matrices with exponential off-diagonal decay.

Results apply to hyperbolic, weakly hyperbolic, and parabolic equations.

Numerical experiments support theoretical findings.

Abstract

We perform a Gabor analysis for a large class of evolution equations with constant coefficients. We show that the corresponding propagators have a very sparse Gabor matrix, displaying off-diagonal exponential decay. The results apply to hyperbolic, weakly hyperbolic and parabolic equations. Some numerical experiments are provided.