## 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)

## Abstract

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 su*q*(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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## BibTeX

@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 = {https://doi.org/10.1016/j.jmaa.2005.08.067}, }