Abstract
We characterize the extremal measures of an indeterminate moment problem associated with a system of orthogonal polynomials defined by a three-term recurrence relation.
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W. A. Al-Salam, T. S. Chihara (1976).:Convolutions of orthogonal polynomials. SIAM J. Math. Anal.,7: 16–28.
R. A. Askey, M. E. H. Ismail (1984):Recurrence relations, continued fractions and orthogonal polynomials. Mem. Amer. Math. Soc.,49: no. 300.
R. A. Askey, J. A. Wilson (1985):Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Mem. Amer. Math. Soc.,54: no. 319.
G. Gasper, M. Rahman (1990): Basic Hypergeometric Series. Encyclopedia of Mathematics and Its Applications vol. 35. Cambridge: Cambridge University Press.
M. E. H. Ismail, D. R. Masson (to appear)Q-Hermite polynomials, biorthogonal rational functions and q-beta integrals.
D. Moak (1981):The q-analogue of the Laguerre polynomials. J. Math. Anal. Appl..,81: 20–47.
F. W. J. Olver (1974).: Asymptotics and Special Functions. New York: Academic Press.
J. Shohat, J. D. Tamarkin (1963): The Problem of Moments. Mathematical Surveys, No. 1. Providence, RI: American Mathematical Society.
G. Szegö (1975): Orthogonal Polynomials, 4th edn. Colloquium Publications vol. XXIII. Providence, RI: American Mathematical Society.
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Communicated by Edward B. Saff.
Dedicated to Waleed Al-Salam on the occasion of his 65th birthday
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Chihara, T.S., Ismail, M.E.H. Extremal measures for a system of orthogonal polynomials. Constr. Approx 9, 111–119 (1993). https://doi.org/10.1007/BF01229339
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DOI: https://doi.org/10.1007/BF01229339