Email this article Spectral deformation in a problem of singular perturbation theory
- Authors: Stepin S.A.1, Fufaev V.V.1
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Affiliations:
- Lomonosov Moscow State University
- Issue: Vol 484, No 4 (2019)
- Pages: 397-400
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/12544
- DOI: https://doi.org/10.31857/S0869-56524844397-400
- ID: 12544
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Abstract
Quasi-classical asymptotic behavior of the spectrum of a non-self-adjoint Sturm–Liouville problem is studied in the case of a one-parameter family of potentials being third-degree polynomials. For this problem, the phase-integral method is used to derive quantization conditions characterizing the asymptotic distribution of the eigenvalues and their concentration near edges of the limit spectral complex. Topologically different types of limit configurations are described, and critical values of the deformation parameter corresponding to type changes are specified.
About the authors
S. A. Stepin
Lomonosov Moscow State University
Author for correspondence.
Email: ststepin@mail.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991
V. V. Fufaev
Lomonosov Moscow State University
Email: ststepin@mail.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991
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