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.

300px-SquareLattice.svgIn 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?