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Differential Operators and Related Topics pp 267–271Cite as

Birkhäuser

Homogeneity of a String having Three Unperturbed Spectra

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 117))

Abstract

We prove that there does not exist a smooth inhomogeneous string such the spectra of three particular boundary value problems describing its small vibrations coincide with those for a homogeneous string. These three boundary value problems are the Dirichlet problem on [0, 1/2],the Dirichlet problem on [1/2, l] ,and the Dirichlet-Neumann problem on[0, l].

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References

  1. R. Courant and D. Hilbert, Methods of Mathematical Physics, vol. 1, Interscience, New York, 1953.

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  5. V.N. Pivovarchik, An Inverse Sturm-Liouville problem by Three Spectra, to appear in Integral Equations and Operator Theory.

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  6. F. Gesztesy and B. Simon, On the Determination of a Potential from Three Spectra, to appear in Birman Birthday Volume in Advances in Mathematical Sciences.

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Author information

Authors and Affiliations

  1. Preobrazhenskaya str, 59/61, a.17, 270045, Odessa, Ukraine

    Vyacheslav N. Pivovarchik

Authors
  1. Vyacheslav N. Pivovarchik
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Editor information

Editors and Affiliations

  1. Department of Theoretical Physics, University of Odessa, 270026, Odessa, Ukraine

    V. M. Adamyan

  2. Department of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Ramat Aviv, Israel

    I. Gohberg

  3. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    M. Gorbachuk  & V. Gorbachuk  & 

  4. Department of Mathematics, Vrije Universiteit, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    M. A. Kaashoek

  5. Department of Mathematics, Technical University of Vienna, Wiedner Hauptstrasse 8-10/1411, 1040, Vienna, Austria

    H. Langer

  6. Institute of Mathematics, Economics and Mechanics, Odessa State University, 270057, Dvoryanskaya str. 2, Odessa, Ukraine

    G. Popov

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© 2000 Springer Basel AG

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Pivovarchik, V.N. (2000). Homogeneity of a String having Three Unperturbed Spectra. In: Adamyan, V.M., et al. Differential Operators and Related Topics. Operator Theory: Advances and Applications, vol 117. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8403-7_19

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  • DOI: https://doi.org/10.1007/978-3-0348-8403-7_19

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9552-1

  • Online ISBN: 978-3-0348-8403-7

  • eBook Packages: Springer Book Archive

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