# Zn

Research on pseudo-differential operators on ${\mathbb Z}^n$ at AIMS Ghana with Master students Linda Botchway and Gaël Kibiti

Botchway L., Kibiti G., Ruzhansky M., Difference equations and pseudo-differential operators on ${\mathbb Z}^n$, arxiv

In this paper one makes a consistent development of the calculus of pseudo-differential operators which can be called pseudo-difference operators in the context of the lattice ${\mathbb Z}^n$ Some interesting questions to answer:

• how to define Hörmander type or other symbol classes on ${\mathbb Z}^n$?
• what is the relation to the analysis on the torus ${\mathbb T}^n$?
• can it be used to derive new properties of operators on ${\mathbb Z}^n$?
• how to apply it to solving difference equations and to finding properties of their solutions?