On the localization of the spectrum of some perturbations of a two-dimensional harmonic oscillator
Kanguzhin B. Fazullin Z.
2021Taylor and Francis Ltd.
Complex Variables and Elliptic Equations
2021#66Issue 6-71194 - 1208 pp.
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 Greens function of a two-dimensional harmonic oscillator is obtained. The singularities of Greens 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.
31A25 , 32A20 , 32A50 , 35J08 , 35J25 , 35P15 , 35P20 , asymptotic distributions of eigenvalues in context of PDEs , boundary value problems for second-order elliptic equations , estimates of eigenvalues in the context of PDEs , Greens functions for elliptic equations , harmonic analysis of several complex variables , meromorphic functions of several complex variables
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Department of Mathematics, Al-Farabi Kazakh National University, Almaty, Kazakhstan
Physical and Mathematical Department, Bashkir State University, Ufa, Russian Federation
Department of Mathematics
Physical and Mathematical Department
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