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On Some Properties of Infinite-dimensional Elliptic Coordinates

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Methods of Spectral Analysis in Mathematical Physics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 186))

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Abstract

A number of the equations in classical mechanics is integrable in Jacobi elliptic coordinates. In recent years a generalization of elliptic coordinates to the infinite case has been offered. We consider this generalization and indicate the connection of infinite-dimensional elliptic coordinates with some inverse spectral problems for infinite Jacobi matrices and sturm-Liouville operators (two spectra inverse problems). Also a link with the rank one perturbation theory is shown.

This work has been supported by the Russian Foundation For Basic Research: project 05-01-00989 and by the Ministry for Science and Technology of Russia: project NSh-5247. 2006.1.

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Author information

Authors and Affiliations

  1. Scientific-Research Institute for System Studies, Russian Academy of Sciences (NIISI RAN), Nakhimovskii pr. 36-1, Moscow, 117218, Russia

    Andrey Osipov

Authors
  1. Andrey Osipov
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Editor information

Editors and Affiliations

  1. Institut of Mathematics, Polish Academy of Sciences, ul. Sw. Tomasza 30/7, 31-027, Krakow, Poland

    Jan Janas

  2. Department of Mathematics, Lund Institute of Technology, 221 00, Lund, Sweden

    Pavel Kurasov

  3. Department of Mathematical Physics, St. Petersburg State University, Ulyanovskaya 1, 198904, St. Petersburg, Russia

    Sergei Naboko

  4. Department of Mathematics South Kensington Campus, Imperial College London, SW7 2AZ, London, UK

    Ari Laptev

  5. Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden

    Ari Laptev

  6. Department of Mathematics, University of Alabama, 452 Campbell Hall, Birmingham, AL, 35294-1170, USA

    GĂĽnter Stolz

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© 2008 Birkhäuser Verlag Basel/Switzerland

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Osipov, A. (2008). On Some Properties of Infinite-dimensional Elliptic Coordinates. In: Janas, J., Kurasov, P., Naboko, S., Laptev, A., Stolz, G. (eds) Methods of Spectral Analysis in Mathematical Physics. Operator Theory: Advances and Applications, vol 186. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8755-6_17

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