Division problem for spatially periodic distributions

TL;DR

This paper establishes a sufficient condition for the surjectivity of certain constant-coefficient partial differential operators acting on distributions that are periodic in space and tempered in time, advancing understanding of such operators.

Contribution

It introduces a new sufficient condition for surjectivity of PDE operators on spatially periodic, tempered distributions, expanding the theoretical framework for these operators.

Findings

Provides a criterion for surjectivity of PDEs on periodic distributions.

Extends the theory of PDE operators to spatially periodic and tempered distributions.

Enhances understanding of the structure of solutions in this distribution class.

Abstract

We give a sufficient condition for the surjectivity of partial differential operators with constant coefficients on a class of distributions on R^{n+1} (here we think of there being n space directions and one time direction), that are periodic in the spatial directions and tempered in the time direction.