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Funktsional'nyi Analiz i ego Prilozheniya, 2025, Volume 59, Issue 3, Pages 49–63
DOI: https://doi.org/10.4213/faa4311 (Mi faa4311) 		 
Eigenvalues of non-selfadjoint functional difference operators

Anna Zernovaa, Alexei Ilyinb, Ari Laptevca, Lukas Schimmerd

a 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
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DOI: https://doi.org/10.4213/faa4311
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.
Received: 08.04.2025
Revised: 25.04.2025
Accepted: 28.04.2025
Published: 11.08.2025
English version:
Functional Analysis and Its Applications, 2025, Volume 59, Issue 3, Pages 258–270
DOI: https://doi.org/10.1134/S1234567825030048
Bibliographic databases:
Document Type: Article
MSC: 47A75, 34L15, 47B39
Language: Russian
Citation: Anna Zernova, Alexei Ilyin, Ari Laptev, Lukas Schimmer, “Eigenvalues of non-selfadjoint functional difference operators”, Funktsional. Anal. i Prilozhen., 59:3 (2025), 49–63; Funct. Anal. Appl., 59:3 (2025), 258–270
Citation in format AMSBIB
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