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On New Relations Between Spectral Properties of Jacobi Matrices and Their Coefficients

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Abstract

We study the spectral properties of Jacobi matrices. By using ``higher order'' trace formulae we obtain a result relating the properties of the elements of Jacobi matrices and the corresponding spectral measures. Complicated expressions for traces of some operators can be magically simplified allowing us to apply induction arguments. Our theorems are generalizations of a recent result of R. Killip and B. Simon [17].

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Authors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology, 10044, Stockholm, Sweden

    A. Laptev & O. Safronov

  2. Department of Physics, University of St. Petersburg, 198904, St. Petersburg, Russia

    S. Naboko

Authors
  1. A. Laptev
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  2. S. Naboko
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  3. O. Safronov
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Correspondence to A. Laptev.

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Communicated by B. Simon

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Laptev, A., Naboko, S. & Safronov, O. On New Relations Between Spectral Properties of Jacobi Matrices and Their Coefficients. Commun. Math. Phys. 241, 91–110 (2003). https://doi.org/10.1007/s00220-003-0924-3

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  • DOI: https://doi.org/10.1007/s00220-003-0924-3

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