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New Proof of Trace Formulas in Case of Classical Sturm-Liouville Problem

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New Results in Operator Theory and Its Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 98))

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Abstract

A generalized trace formula for Sturm-Liouville operators is proved using the method of the wave equation.

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References

  1. I. M. Gelfand and B. M. Levitan. On a simple identity for the eigenvalues of a differential operator of second order. Dokl. Akad. Nauk USSR 88, (1953), 593–596.

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  2. B. M. Levitan. On the asymptotic behavior of the spectral function of a self-adjoint differential equation of second order. Izv. Akad. Nauk USSR, Serie Math. 16 (1952), 325–352. English translation: Amer. Math. Soc. Transl. (2) 101 (1973), 192-221.

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  3. B. M. Levitan. On the asymptotic behavior of the spectral function of a self-adjoint differential operator of second order. Izv. Akad. Nauk USSR, Serie Math. 17 (1953), 331–364. English translation:Amer.Math. Soc. Transl. 102 (1973), 191-229.

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Author information

Authors and Affiliations

  1. School of Mathematics, University of Minneapolis, 127 Vincent Hall, 206 Church Str. S.E., Minneapolis, MN, 55455, USA

    B. M. Levitan

Authors
  1. B. M. Levitan
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Editor information

Editors and Affiliations

  1. Raymond and Beverly Sackler Faculty of Exact Sciences School of Mathematical Sciences, Tel Aviv University, IL-69978, Tel Aviv, Israel

    I. Gohberg  & Yu. Lyubich  & 

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© 1997 Springer Basel AG

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Levitan, B.M. (1997). New Proof of Trace Formulas in Case of Classical Sturm-Liouville Problem. In: Gohberg, I., Lyubich, Y. (eds) New Results in Operator Theory and Its Applications. Operator Theory: Advances and Applications, vol 98. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8910-0_11

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  • DOI: https://doi.org/10.1007/978-3-0348-8910-0_11

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9824-9

  • Online ISBN: 978-3-0348-8910-0

  • eBook Packages: Springer Book Archive

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