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Funktsional'nyi Analiz i ego Prilozheniya, 2014, Volume 48, Issue 3, Pages 88–92
DOI: https://doi.org/10.4213/faa3153
(Mi faa3153)
 

Brief communications

Spectral Analysis of Indefinite Sturm–Liouville Operators

A. S. Kostenko

Faculty of Mathematics, University of Vienna
References:
Abstract: For a class of indefinite $J$-nonnegative Sturm–Liouville operators, we present a criterion of similarity to a self-adjoint operator. This criterion is formulated in terms of Weyl–Titchmarsh $m$-functions. Moreover, using this result, we obtain a criterion, as well as simple sufficient conditions, formulated in terms of the coefficients of a given Sturm–Liouville operator.
Keywords: Sturm–Liouville operator, $J$-nonnegative operator, critical point, similarity to a self-adjoint operator.
Funding agency Grant number
Austrian Science Fund M1309-N13
Received: 11.07.2012
English version:
Functional Analysis and Its Applications, 2014, Volume 48, Issue 3, Pages 227–230
DOI: https://doi.org/10.1007/s10688-014-0064-x
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: A. S. Kostenko, “Spectral Analysis of Indefinite Sturm–Liouville Operators”, Funktsional. Anal. i Prilozhen., 48:3 (2014), 88–92; Funct. Anal. Appl., 48:3 (2014), 227–230
Citation in format AMSBIB
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  • https://doi.org/10.4213/faa3153
  • https://www.mathnet.ru/eng/faa/v48/i3/p88
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    Функциональный анализ и его приложения Functional Analysis and Its Applications
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