Wavefront sets of convolutions of distributions with (weighted) line integral

TL;DR

This paper investigates the wavefront sets of convolutions involving distributions defined by line integrals, focusing on how singularities propagate and scatter in these convolutions.

Contribution

It provides new insights into the behavior of wavefront sets under convolution with line integral distributions, including the effects of weights.

Findings

Characterization of wavefront set scattering

Analysis of singularity propagation in convolutions

Extension of convolution theory to weighted line integral distributions

Abstract

In this article, we explore convolutions of distributions with distributions given by (weighted) line integration. We also explore the scattering of singularities of such convolutions.