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Scattering in a Loop-shaped Waveguide

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Recent Advances in Operator Theory

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 124))

Abstract

Wave scattering is considered in a loop-shaped one-dimensional waveguide. For finite potential the problem can be reduced to a Regge type one. The conditions are obtained sufficient for a function to be the S-matrix of a problem of the class considered. The algorithm of recovering the potential from given Jost function is presented. It is shown that the solution of this inverse problem is not unique.

Dedicated to Israel Gohberg on the occasion of his 70-th birthday

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References

  1. V. Adamyan, Scattering matrices for Microschemes, Operator Theory: Advances and Appl. 59 (1992), 1–10.

    MathSciNet  Google Scholar 

  2. V.M. Adamyan and B.S. Pavlov, Null-Range Potentials and M.G. Krein’s Formula of Generalized Resolvents (Russian), Studies on Linear Operators of Functions. IV. Research Notes of Scientific Seminar of the LBMI 149 (1986), 7–23.

    MATH  Google Scholar 

  3. P. Exner and P. Seba,A New Type of Quantum Interference Transistor Phys. Lett . A 129:8, 9 (1988), 477–480.

    MathSciNet  Google Scholar 

  4. N.I. Gerasimenko, Inverse Scattering Problem on Noncompact Graph (Russian), Teoreticheskaya i matematicheskaya fisika 75:2 (1988), 187–200.

    MathSciNet  Google Scholar 

  5. N.I. Gerasimenko and B.S. Pavlov, Scattering Problem on Noncompact Graphs (Russian), Teoreticheskaya i matematicheskaya fisika 74:3 (1988), 345–359.

    MathSciNet  Google Scholar 

  6. I.C. Gohberg and M.G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators, Amer. Math. Soc, Providence, 1969.

    MATH  Google Scholar 

  7. B.Ya. Levin, Lectures on Entire Functions, Translations of Mathematical Monographs, AMS 150 (1996).

    MATH  Google Scholar 

  8. B.Ya. Levin and Yu.I. Lyubarskii, Interpolation by Entire Functions of Special Classes and Related Expansions in Series of Exponents (Russian), Izv. Akad. Nauk USSR, Sec. Mat. 43 (1979), 87–110.

    Google Scholar 

  9. V.A. Marchenko, Sturm-Liouville Operators and Applications, Birkhauser, OT 22 (1986).

    Google Scholar 

  10. R.G. Newton, Scattering Theory of Waves and Particles, McGraw-Hill, New York 1966.

    Google Scholar 

  11. V. Pivovarchik, On Positive Spectra of One Class of Polynomial Operator Pencils, Integral Equations and Operator Theory 19 (1994), 314–326.

    Article  MathSciNet  MATH  Google Scholar 

  12. T. Regge, Construction of Potential from Resonances, Nuovo Cimento 9:3, 5 (1958), 491–503,671–679.

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

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

    Vyacheslav Pivovarchik

Authors
  1. Vyacheslav Pivovarchik
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV, Groningen, The Netherlands

    A. Dijksma

  2. Division of Mathematics and Computer Science Faculty of Sciences, Vrije Universiteit, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    M. A. Kaashoek  & A. C. M. Ran  & 

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© 2001 Springer Basel AG

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Pivovarchik, V. (2001). Scattering in a Loop-shaped Waveguide. In: Dijksma, A., Kaashoek, M.A., Ran, A.C.M. (eds) Recent Advances in Operator Theory. Operator Theory: Advances and Applications, vol 124. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8323-8_24

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  • DOI: https://doi.org/10.1007/978-3-0348-8323-8_24

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9516-3

  • Online ISBN: 978-3-0348-8323-8

  • eBook Packages: Springer Book Archive

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