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?

Michael Ruzhansky

Michael Ruzhansky, Senior Full Professor of Mathematics, Ghent University, and Professor of Mathematics, Queen Mary University of London

Lattice Zn

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