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 Zap. Nauchn. Sem. POMI, 2015, Volume 433, Pages 111–130 (Mi znsl6129)

The discrete spectrum of Jacobi matrix related to recurrence relations with periodic coefficients

V. V. Borzova, E. V. Damaskinskyb

a St. Petersburg State University of Telecommunications, St. Petersburg, Russia
b Military Technical Institute, St. Petersburg, Russia

Abstract: In this note we investigate the discrete spectrum of Jacobi matrix corresponding to polynomials defined by recurrence relations with periodic coefficients. As examples we consider
a) the case when period $N$ of coefficients of recurrence relations equals three (as a particular case we consider “parametric” Chebyshev polynomials introduced by authors early);
b) the elementary $N$-symmetrical Chebyshev polynomials ($N=3,4,5$), that was introduced by authors in the study of the “composite model of generalized oscillator”.

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English version:
Journal of Mathematical Sciences (New York), 2016, 213:5, 694–705

Bibliographic databases:

UDC: 517.9

Citation: V. V. Borzov, E. V. Damaskinsky, “The discrete spectrum of Jacobi matrix related to recurrence relations with periodic coefficients”, Questions of quantum field theory and statistical physics. Part 23, Zap. Nauchn. Sem. POMI, 433, POMI, St. Petersburg, 2015, 111–130; J. Math. Sci. (N. Y.), 213:5 (2016), 694–705

Citation in format AMSBIB
\Bibitem{BorDam15} \by V.~V.~Borzov, E.~V.~Damaskinsky \paper The discrete spectrum of Jacobi matrix related to recurrence relations with periodic coefficients \inbook Questions of quantum field theory and statistical physics. Part~23 \serial Zap. Nauchn. Sem. POMI \yr 2015 \vol 433 \pages 111--130 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl6129} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3493682} \transl \jour J. Math. Sci. (N. Y.) \yr 2016 \vol 213 \issue 5 \pages 694--705 \crossref{https://doi.org/10.1007/s10958-016-2732-2} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84957707945}