Paper: Limit relations between q-Krall type orthogonal polynomials

Limit relations between q-Krall type orthogonal polynomials

Álvarez-Nodarse, R. and Costas-Santos, R. S. Journal of Mathematical Analysis and Applications 322, no. 1 (2006), 158 — 176

ACADEMIC PRESS INC ELSEVIER SCIENCE (USA) | ISSN: 0022-247X | JCR┬« 2006 Impact Factor: 0.758 - MATHEMATICS — position: 46/187 (Q1/T1)


We argue that one can factorize the difference equation of hypergeometric type on the non-uniform lattices in general case. It is shown that in the most cases of q-linear spectrum of the eigenvalues this directly leads to the dynamical symmetry algebra suq(1,1), whose generators are explicitly constructed in terms of the difference operators, obtained in the process of factorization. Thus all models with the q-linear spectrum (some of them, but not all, previously considered in a number of publications) can be treated in a unified form.


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@article {MR2238156,
AUTHOR = {Álvarez-Nodarse, R. and Costas-Santos, R. S.},
TITLE = {Limit relations between {$q$}-{K}rall type orthogonal polynomials},
JOURNAL = {J. Math. Anal. Appl.},
FJOURNAL = {Journal of Mathematical Analysis and Applications},
VOLUME = {322},
YEAR = {2006},
NUMBER = {1},
PAGES = {158--176},
ISSN = {0022-247X},
MRCLASS = {33C45 (42C05)},
ZBL = {1096.33011},
MRNUMBER = {2238156},
MRREVIEWER = {Youss\`ef Ben Cheikh},
DOI = {10.1016/j.jmaa.2005.08.067},
URL = {},
Date: 2021/11/16