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Funktsional. Anal. i Prilozhen., 2014, Volume 48, Issue 3, Pages 88–92 (Mi faa3153)  

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

Funding Agency Grant Number
Austrian Science Fund M1309-N13


DOI: https://doi.org/10.4213/faa3153

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English version:
Functional Analysis and Its Applications, 2014, 48:3, 227–230

Bibliographic databases:

UDC: 517.9
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

Citation in format AMSBIB
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