# Linda Botchway starting her PhD

Congratulations to Linda Botchway, for receiving the grant of USD 15,500 from the Carnegie Corporation of New York (CCNY), for her PhD at the University of Ghana, Legon, under our supervision.

Well done, Linda!

We are looking forward to Linda’s visits to our Analysis & PDE Center at Ghent University, and to her enrolment to UGent PhD program for a joint PhD.

Research of Linda on pseudo-differential operators on ${\mathbb Z}^n$ started while she was a Master student at AIMS Ghana. This resulted in a substantial (41 pages) publication, a great achievement for a Master Student:

Botchway L., Kibiti G., Ruzhansky M., Difference equations and pseudo-differential operators on ZnJ. Funct. Anal.278 (2020), no. 11, 108473, 41pp. link (open access)arxiv

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?