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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| Published in: | Complex variables and elliptic equations Vol. 66; no. 6-7; pp. 1194 - 1208 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Colchester
Taylor & Francis
03.07.2021
Taylor & Francis Ltd |
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| ISSN: | 1747-6933, 1747-6941 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Kanguzhin, Baltabek Fazullin, Ziganur |
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| Copyright | 2021 Informa UK Limited, trading as Taylor & Francis Group 2021 2021 Informa UK Limited, trading as Taylor & Francis Group |
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| Snippet | In this paper, we study the localization of the discrete spectrum of certain perturbations of a two-dimensional harmonic oscillator. The convergence of the... |
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| SubjectTerms | 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 |
| Title | On the localization of the spectrum of some perturbations of a two-dimensional harmonic oscillator |
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