Work

Convolution Type Operators With Potential: Essential and Infinite Discrete Spectrum

Year: 2025

Type: article

Abstract: ABSTRACT The goal of this note is to study the spectrum of a self‐adjoint convolution operator in with an integrable kernel that is perturbed by an essentially bounded real‐valued potential tending to zero at infinity. We show that the essential spectrum of such operator is the union of the spectrum of the convolution operator and of the essential range of the potential. Then we provide several sufficient conditions for the existence of a countable sequence of discrete eigenvalues. For operators having nonconnected essential spectrum, we give sufficient conditions for the existence of discrete eigenvalues in the corresponding gaps of the essential spectrum.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.10745

Authors: Denis Borisov, Andrey Piatnitski, Elena Zhizhina

Institutions: Peoples' Friendship University of Russia, Russian Academy of Sciences, Institute of Mathematics with Computer Center, Moscow Institute of Physics and Technology, UiT The Arctic University of Norway

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: Tromsø Forskningsstiftelse, Ministry of Science and Higher Education of the Russian Federation

Awards: G5703249084, G597338630, G6444257319