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A Functional Model, Eigenvalues, and Finite Singular Critical Points for Indefinite Sturm-Liouville Operators

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Book cover Topics in Operator Theory

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 203))

Abstract

Eigenvalues in the essential spectrum of a weighted Sturm-Liouville operator are studied under the assumption that the weight function has one turning point. An abstract approach to the problem is given via a functional model for indefinite Sturm-Liouville operators. Algebraic multiplicities of eigenvalues are obtained. Also, operators with finite singular critical points are considered.

This work was partly supported by the PIMS Postdoctoral Fellowship at the University of Calgary.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, T2N 1N4, Alberta, Canada

    I. M. Karabash

  2. Department of PDE, Institute of Applied Mathematics and Mechanics, R. Luxemburg str. 74, Donetsk, 83114, Ukraine

    I. M. Karabash

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  1. I. M. Karabash
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Editors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061, USA

    Joseph A. Ball

  2. Department of Mathematics, College of William and Mary, P. O. Box 8795, Williamsburg, VA, 23187-8795, USA

    Vladimir Bolotnikov , Leiba Rodman  & Ilya M. Spitkovsky ,  & 

  3. Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0112

    J. William Helton

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Dedicated to Israel Gohberg on the occasion of his eightieth birthday

Communicated by J.A. Ball.

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Karabash, I.M. (2010). A Functional Model, Eigenvalues, and Finite Singular Critical Points for Indefinite Sturm-Liouville Operators. In: Ball, J.A., Bolotnikov, V., Rodman, L., Spitkovsky, I.M., Helton, J.W. (eds) Topics in Operator Theory. Operator Theory: Advances and Applications, vol 203. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0161-0_11

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