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Spectral analysis of a differential operator with an involution

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Abstract

We use the method of similar operators to perform the asymptotic analysis of the spectrum of a differential operator with an involution. We show that such operators have compact resolvent, and that their large eigenvalues are determined by the values of (the Fourier coefficients) of their potential up to a summable sequence.

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Authors and Affiliations

  1. Department of Applied Mathematics and Mechanics, Voronezh State University, Voronezh, 394693, Russia

    Anatoly G. Baskakov & Elena Yu. Romanova

  2. Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL, 60115, USA

    Ilya A. Krishtal

Authors
  1. Anatoly G. Baskakov
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  2. Ilya A. Krishtal
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  3. Elena Yu. Romanova
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Correspondence to Ilya A. Krishtal.

Additional information

Anatoly G. Baskakov is supported in part by RFBR Grant 16-01-00197 and RSF Grant 14-21-00066 (Section 4). Ilya A. Krishtal is supported in part by NSF Grant DMS-1322127.

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Baskakov, A.G., Krishtal, I.A. & Romanova, E.Y. Spectral analysis of a differential operator with an involution. J. Evol. Equ. 17, 669–684 (2017). https://doi.org/10.1007/s00028-016-0332-8

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