An excursion to multiplications and convolutions on modulation spaces

Abstract

We give a self-contained introduction to (quasi-)Banach modulation spaces of ultradistributions, and review results on boundedness for multiplications and convolutions for elements in such spaces. Furthermore, we use these results to study the Gabor product. As an example, we show how it appears in a phase-space formulation of the nonlinear cubic Schrödinger equation.

This is aimed as a survey paper. Especially we present some convolution results which are special cases of the arXiv paper with the arXiv number 2011.06941 . The paper consists of 29 pages