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Discrete Spectrum of the Jacobi Matrix Related to Recurrence Relations with Periodic Coefficients

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In this note, we study the discrete spectrum of the Jacobi matrix corresponding to polynomials defined by recurrence relations with periodic coefficients. As examples, we consider

(a) the case where the period N of coefficients of recurrence relations equals 3 (as a particular case, we consider “parametric” Chebyshev polynomials introduced by the authors earlier);

(b) elementary N-symmetric Chebyshev polynomials (N = 3, 4, 5), which were introduced by the authors in the study of the “composite model of a generalized oscillator.”

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Authors and Affiliations

  1. St.Petersburg University of Telecommunications, St.Petersburg, Russia

    V. V. Borzov

  2. St.Petersburg Military Engineering-Technical University, St.Petersburg, Russia

    E. V. Damaskinsky

Authors
  1. V. V. Borzov
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  2. E. V. Damaskinsky
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Corresponding author

Correspondence to V. V. Borzov.

Additional information

Dedicated to Petr Kulish in connection with the seventieth anniversary

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 433, 2015, pp. 111–130.

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Borzov, V.V., Damaskinsky, E.V. Discrete Spectrum of the Jacobi Matrix Related to Recurrence Relations with Periodic Coefficients. J Math Sci 213, 694–705 (2016). https://doi.org/10.1007/s10958-016-2732-2

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