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Multithreshold Spectral Phase Transitions for a Class of Jacobi Matrices

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Recent Advances in Operator Theory

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

Abstract

Consider an arbitrary periodic Jacobi matrix J per ,with periodic weights c n . A class of unbounded Jacobi matrices A + cB is investigated, where B is a diagonal matrix and A is a Jacobi matrix with zero main diagonal and modulated weights λ n (e.g. λ n = c n n α, α > 0). Depending on whether the coupling constant (-c) belongs to the absolutely continuous spectrum of J per or not, the spectrum of A + cB is either pure absolutely continuous or discrete. This gives us a class of examples with multithreshold spectral phase transition phenomena.

Dedicated to Professor Israel Gohberg on the occasion of his seventieth birthday

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, Cracow Branch Sw. Tomasza 30, 31-027, Cracow, Poland

    J. Janas

  2. Department of Mathematical Physics Institute of Physics, St. Petersburg University, Ulianovskaia 1 St. Petergoff, S. Petersburg, Russia, 198904

    S. Naboko

Authors
  1. J. Janas
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  2. S. Naboko
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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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Janas, J., Naboko, S. (2001). Multithreshold Spectral Phase Transitions for a Class of Jacobi Matrices. 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_13

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  • DOI: https://doi.org/10.1007/978-3-0348-8323-8_13

  • 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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