Work

Spectral asymptotics for Schrodinger operator perturbed by translation operator

Year: 2025

Type: article

Abstract: We consider the one-dimensional Schrödinger operator on the unit segment with Dirichlet condition and perturb it by a translation operator. The main result describes the asymptotics of the eigenvalues of this operator with respect to the index counting the eigenvalues, the resulting asymptotics is uniform in the translation. In the asymptotics, we explicitly find the terms generated by the translation operator. We establish that the system of eigenfunctions and generalized eigenfunctions of the considered operator forms a Bari basis in the space of functions square integrable on the unit segment.

Source: Izvestiya Mathematics

DOI: 10.4213/im9574e

Authors: Denis Ivanovich Borisov, Dmitry Mikhailovich Polyakov

Institutions: Russian Academy of Sciences, Institute of Mathematics with Computer Center, Federal State Budgetary Institution of Science Federal Scientific Center "Vladikavkaz Scientific Center of the Russian Academy of Sciences"

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Russian Science Foundation

Award: G19369174