The filter of singularities in global anisotropic microlocal analysis

TL;DR

This paper introduces a new filter for anisotropic singularities in phase space, extending the Gabor wave front set, and demonstrates its propagation in certain Schrödinger-type equations.

Contribution

It defines a novel anisotropic singularity filter in phase space and proves propagation results for linear evolution equations of Schrödinger type.

Findings

The filter captures anisotropic singularities in tempered distributions.

Propagation results are established for Schrödinger-type equations.

The filter generalizes the harmonic oscillator case.

Abstract

We define a filter of time-frequency anisotropic global singularities of phase space for tempered distributions. The filter contains information from the corresponding anisotropic Gabor wave front set and admits propagation results for the Cauchy problem for certain linear evolution equations of Schr\"odinger type that generalize the harmonic oscillator.