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On the asymptotics of the spectrum of a nonsemibounded vector Sturm-Liouville operator

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Abstract

On the half-line, we consider a vector Sturm-Liouville operator with a potential that is unbounded below. Asymptotic formulas for the spectrum are given. These formulas involve the eigenvalues of the matrix potential as well as the “rotational velocities” of the eigenvectors.

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Authors and Affiliations

  1. Bauman Moscow State Technical University, Russia

    R. S. Ismagilov & A. G. Kostyuchenko

Authors
  1. R. S. Ismagilov
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  2. A. G. Kostyuchenko
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Correspondence to R. S. Ismagilov.

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__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 42, No. 2, pp. 11–22, 2008

Original Russian Text Copyright © by R. S. Ismagilov and A. G. Kostyuchenko

The first author was supported by RFBR grants nos. 07-01-91209YaF_a and 07-01-00283 and by grant NSh 2372.2008.1. The second author was supported by RFBR grant no. 07-01-00283 and by grant NSh 2372.2008.1.

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Ismagilov, R.S., Kostyuchenko, A.G. On the asymptotics of the spectrum of a nonsemibounded vector Sturm-Liouville operator. Funct Anal Its Appl 42, 89–97 (2008). https://doi.org/10.1007/s10688-008-0014-6

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  • DOI: https://doi.org/10.1007/s10688-008-0014-6

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