Eigenvalues of non-selfadjoint functional difference operators

Anna Zernova^a, Alexei Ilyin^b, Ari Laptev^ca, Lukas Schimmer<sup>d

a</sup> University of Science and Technology "Sirius", Sochi, Russia
^b Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow, Russia
^c Imperial College London, Department of Mathematics, London, United Kingdom
^d Department of Mathematical Sciences, Loughborough University, Loughborough, United Kingdom

Abstract: Using the well known approach developed in the papers of B. Davies and his co-authors, we obtain inequalities for the location of possible complex eigenvalues of non-selfadjoint functional difference operators. When studying the sharpness of the main result, we discovered that complex potentials can create resonances.

Keywords: complex eigenvalues, Birman–Schwinger principle, Weyl operators, Jost solutions.

MSC: 47A75, 34L15, 47B39

Received: 08.04.2025
Revised: 25.04.2025
Accepted: 28.04.2025

DOI: 10.4213/faa4311

 English version: Functional Analysis and Its Applications, 2025, 59:3, 258–270

Bibliographic databases:

• 
• 
•