$N$-symmetric Chebyshev polynomials in a~composite model of a~generalized oscillator
Teoretičeskaâ i matematičeskaâ fizika, Tome 169 (2011) no. 2, pp. 229-240
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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 $N\ge6$.
Keywords:
generalized oscillator, Chebyshev polynomial, classical moment problem.
@article{TMF_2011_169_2_a4,
author = {V. V. Borzov and E. V. Damaskinsky},
title = {$N$-symmetric {Chebyshev} polynomials in a~composite model of a~generalized oscillator},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {229--240},
publisher = {mathdoc},
volume = {169},
number = {2},
year = {2011},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2011_169_2_a4/}
}
TY - JOUR AU - V. V. Borzov AU - E. V. Damaskinsky TI - $N$-symmetric Chebyshev polynomials in a~composite model of a~generalized oscillator JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2011 SP - 229 EP - 240 VL - 169 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2011_169_2_a4/ LA - ru ID - TMF_2011_169_2_a4 ER -
%0 Journal Article %A V. V. Borzov %A E. V. Damaskinsky %T $N$-symmetric Chebyshev polynomials in a~composite model of a~generalized oscillator %J Teoretičeskaâ i matematičeskaâ fizika %D 2011 %P 229-240 %V 169 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2011_169_2_a4/ %G ru %F TMF_2011_169_2_a4
V. V. Borzov; E. V. Damaskinsky. $N$-symmetric Chebyshev polynomials in a~composite model of a~generalized oscillator. Teoretičeskaâ i matematičeskaâ fizika, Tome 169 (2011) no. 2, pp. 229-240. http://geodesic.mathdoc.fr/item/TMF_2011_169_2_a4/