On the asymptotics of spectrum of an even-order differential operator with a delta-function potential

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Abstract

We study a sequence of differential operators of high even order whose potentials converge to the Dirac delta-function. One of the types of separated boundary conditions is considered. At the points of potential discontinuity, it is necessary to study the conditions of gluing for the correct determination of the corresponding differential equations solutions. For large values of the spectral parameter, asymptotic solutions of differential equations are furnished by the Naimark method. The conditions of gluing are studied, the boundary conditions are investigated, the equation for the eigenvalues of the considered differential operator is derived. The method of successive approximations is used to find the asymptotics of spectrum of studied differential operators, the limit of which determines a spectrum of operator with a delta-function potential.

About the authors

Sergei I. Mitrokhin

Lomonosov Moscow State University, Research Computing Center

Author for correspondence.
Email: mitrokhin-sergey@yandex.ru
ORCID iD: 0000-0003-1896-0563
Scopus Author ID: 7004215463
http://www.mathnet.ru/person46310

Cand. Phys. & Math. Sci., Associate Professor; Senior Researcher; Research Computing Center

1, Leninskie Gory, Moscow, 119991, Russian Federation

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