Geodesic
The discrete spectrum of Jacobi matrix related to recurrence relations with periodic coefficients
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 23, Tome 433 (2015), pp. 111-130

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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”. 
@article{ZNSL_2015_433_a5,
     author = {V. V. Borzov and E. V. Damaskinsky},
     title = {The discrete spectrum of {Jacobi} matrix related to recurrence relations with periodic coefficients},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {111--130},
     publisher = {mathdoc},
     volume = {433},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_433_a5/}
}
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V. V. Borzov; E. V. Damaskinsky. The discrete spectrum of Jacobi matrix related to recurrence relations with periodic coefficients. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 23, Tome 433 (2015), pp. 111-130. http://geodesic.mathdoc.fr/item/ZNSL_2015_433_a5/