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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Vydané v:	Complex variables and elliptic equations Ročník 66; číslo 6-7; s. 1194 - 1208
Hlavní autori:	Kanguzhin, Baltabek, Fazullin, Ziganur
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Colchester Taylor & Francis 03.07.2021 Taylor & Francis Ltd
Predmet:	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
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Popis
Shrnutí:	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.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1747-6933 1747-6941
DOI:	10.1080/17476933.2021.1885386