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N-symmetric Chebyshev polynomials in a composite model of a generalized oscillator

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Abstract

We continue to study a composite model of a generalized oscillator generated by an N-periodic Jacobi matrix. The foundation of the model is a system of orthogonal polynomials connected to this matrix for N = 3, 4, 5. We show that such polynomials do not exist for N ≥ 6.

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Authors and Affiliations

  1. Bonch-Bruevich Saint-Petersburg State University of Telecommunications, St. Petersburg, Russia

    V. V. Borzov

  2. Saint 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

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 169, No. 2, pp. 229–240, November, 2011.

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Borzov, V.V., Damaskinsky, E.V. N-symmetric Chebyshev polynomials in a composite model of a generalized oscillator. Theor Math Phys 169, 1561–1572 (2011). https://doi.org/10.1007/s11232-011-0133-8

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  • DOI: https://doi.org/10.1007/s11232-011-0133-8

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