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Brief communications
Spectral Analysis of Indefinite Sturm–Liouville Operators
A. S. Kostenko Faculty of Mathematics, University of Vienna
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.
Received: 11.07.2012
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
Linking options:
https://www.mathnet.ru/eng/faa3153https://doi.org/10.4213/faa3153 https://www.mathnet.ru/eng/faa/v48/i3/p88
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Abstract page: | 401 | Full-text PDF : | 186 | References: | 68 | First page: | 36 |
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