On Infinite Discrete Spectrum of Convolution Operators with Potentials
In $$L_2(\mathbb{R}^d)$$ , we consider a self-adjoint operator which is the sum of a convolution operator and a potential. With minimal assumptions on the convolution kernel and the potential, we describe the location of its essential spectrum and give sufficient conditions for the existence of infinite series of discrete eigenvalues accumulating at the edges of the essential spectrum. We also discuss the case where a non-empty discrete spectrum appears in gaps of the essential spectrum.
Authors
- Andrey Lvovich Piatnitski (ORCID: https://orcid.org/0000-0002-9874-6227)
- D. I. Borisov (ORCID: https://orcid.org/0000-0001-9631-1791)
- Elena Zhizhina
Institutions
- Peoples' Friendship University of Russia (RU)
- Moscow Institute of Physics and Technology (RU)
- Institute of Mathematics with Computer Center (RU)
- M. Akmullah Bashkir State Pedagogical University (RU)
- UiT The Arctic University of Norway (NO)
Publication Details
- Journal
- Functional Analysis and Its Applications
- Published
- 2025-12-01
- DOI
- https://doi.org/10.1134/s123456782504007x
- Primary Topic
- Spectral Theory in Mathematical Physics
- Type
- article
- Field-Weighted Citation Impact
- 0.00