Lattice 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 Zⁿ, J. Funct. Anal., 278 (2020), no. 11, 108473, 41pp. link (open access), arxiv

For more mathematical details see here.

In the above 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?

%d bloggers like this: