On the localization of the spectrum of some perturbations of a two-dimensional harmonic oscillator

In this paper, we study the localization of the discrete spectrum of certain perturbations of a two-dimensional harmonic oscillator. The convergence of the expansion of the source function in terms of the eigenfunctions of a two-dimensional harmonic oscillator is investigated. A representation of Gr...

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Bibliographic Details
Published in:Complex variables and elliptic equations Vol. 66; no. 6-7; pp. 1194 - 1208
Main Authors: Kanguzhin, Baltabek, Fazullin, Ziganur
Format: Journal Article
Language:English
Published: Colchester Taylor & Francis 03.07.2021
Taylor & Francis Ltd
Subjects:
asymptotic distributions of eigenvalues in context of PDEs
boundary value problems for second-order elliptic equations
Eigenvalues
Eigenvectors
estimates of eigenvalues in the context of PDEs
Green's functions
Green's functions for elliptic equations
harmonic analysis of several complex variables
Harmonic oscillators
Localization
meromorphic functions of several complex variables
Perturbation
Well posed problems
ISSN:1747-6933, 1747-6941
Online Access:Get full text
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Summary:In this paper, we study the localization of the discrete spectrum of certain perturbations of a two-dimensional harmonic oscillator. The convergence of the expansion of the source function in terms of the eigenfunctions of a two-dimensional harmonic oscillator is investigated. A representation of Green's function of a two-dimensional harmonic oscillator is obtained. The singularities of Green's function are highlighted. The well-posed definition of the maximal operator generated by a two-dimensional harmonic oscillator on a specially extended domain of definition is given. Then, we describe everywhere solvable invertible restrictions of the maximal operator. We establish that the eigenvalues of a harmonic oscillator will also be the eigenvalues of well-posed restrictions. The results are supported by illustrative examples.
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ISSN:1747-6933
1747-6941
DOI:10.1080/17476933.2021.1885386