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Search: All articles in the CJM digital archive with keyword orthogonal polynomials

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1. CJM 2016 (vol 68 pp. 1159)

Yattselev, Maxim L.
 Strong Asymptotics of Hermite-PadÃ© Approximants for Angelesco Systems In this work type II Hermite-PadÃ© approximants for a vector of Cauchy transforms of smooth Jacobi-type densities are considered. It is assumed that densities are supported on mutually disjoint intervals (an Angelesco system with complex weights). The formulae of strong asymptotics are derived for any ray sequence of multi-indices. Keywords:Hermite-PadÃ© approximation, multiple orthogonal polynomials, non-Hermitian orthogonality, strong asymptotics, matrix Riemann-Hilbert approachCategories:42C05, 41A20, 41A21

2. CJM 2012 (vol 65 pp. 600)

Kroó, A.; Lubinsky, D. S.
 Christoffel Functions and Universality in the Bulk for Multivariate Orthogonal Polynomials We establish asymptotics for Christoffel functions associated with multivariate orthogonal polynomials. The underlying measures are assumed to be regular on a suitable domain - in particular this is true if they are positive a.e. on a compact set that admits analytic parametrization. As a consequence, we obtain asymptotics for Christoffel functions for measures on the ball and simplex, under far more general conditions than previously known. As another consequence, we establish universality type limits in the bulk in a variety of settings. Keywords:orthogonal polynomials, random matrices, unitary ensembles, correlation functions, Christoffel functionsCategories:42C05, 42C99, 42B05, 60B20

3. CJM 2002 (vol 54 pp. 709)

Ismail, Mourad E. H.; Stanton, Dennis
 $q$-Integral and Moment Representations for $q$-Orthogonal Polynomials We develop a method for deriving integral representations of certain orthogonal polynomials as moments. These moment representations are applied to find linear and multilinear generating functions for $q$-orthogonal polynomials. As a byproduct we establish new transformation formulas for combinations of basic hypergeometric functions, including a new representation of the $q$-exponential function $\mathcal{E}_q$. Keywords:$q$-integral, $q$-orthogonal polynomials, associated polynomials, $q$-difference equations, generating functions, Al-Salam-Chihara polynomials, continuous $q$-ultraspherical polynomialsCategories:33D45, 33D20, 33C45, 30E05

4. CJM 1997 (vol 49 pp. 520)

Ismail, Mourad E. H.; Stanton, Dennis
 Classical orthogonal polynomials as moments We show that the Meixner, Pollaczek, Meixner-Pollaczek, the continuous $q$-ultraspherical polynomials and Al-Salam-Chihara polynomials, in certain normalization, are moments of probability measures. We use this fact to derive bilinear and multilinear generating functions for some of these polynomials. We also comment on the corresponding formulas for the Charlier, Hermite and Laguerre polynomials. Keywords:Classical orthogonal polynomials, \ACP, continuous, $q$-ultraspherical polynomials, generating functions, multilinear, generating functions, transformation formulas, umbral calculusCategories:33D45, 33D20, 33C45, 30E05

5. CJM 1997 (vol 49 pp. 175)

Xu, Yuan
 Orthogonal Polynomials for a Family of Product Weight Functions on the Spheres Based on the theory of spherical harmonics for measures invariant under a finite reflection group developed by Dunkl recently, we study orthogonal polynomials with respect to the weight functions $|x_1|^{\alpha_1}\cdots |x_d|^{\alpha_d}$ on the unit sphere $S^{d-1}$ in $\RR^d$. The results include explicit formulae for orthonormal polynomials, reproducing and Poisson kernel, as well as intertwining operator. Keywords:Orthogonal polynomials in several variables, sphere, h-harmonicsCategories:33C50, 33C45, 42C10
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