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Search: All articles in the CJM digital archive with keyword variable

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1. CJM 2010 (vol 63 pp. 200)

Rahman, Mizan
An Explicit Polynomial Expression for a $q$-Analogue of the 9-$j$ Symbols
Using standard transformation and summation formulas for basic hypergeometric series we obtain an explicit polynomial form of the $q$-analogue of the 9-$j$ symbols, introduced by the author in a recent publication. We also consider a limiting case in which the 9-$j$ symbol factors into two Hahn polynomials. The same factorization occurs in another limit case of the corresponding $q$-analogue.

Keywords:6-$j$ and 9-$j$ symbols, $q$-analogues, balanced and very-well-poised basic hypergeometric series, orthonormal polynomials in one and two variables, Racah and $q$-Racah polynomials and their extensions
Categories:33D45, 33D50

2. CJM 2008 (vol 60 pp. 334)

Curry, Eva
Low-Pass Filters and Scaling Functions for Multivariable Wavelets
We show that a characterization of scaling functions for multiresolution analyses given by Hern\'{a}ndez and Weiss and that a characterization of low-pass filters given by Gundy both hold for multivariable multiresolution analyses.

Keywords:multivariable multiresolution analysis, low-pass filter, scaling function
Categories:42C40, 60G35

3. 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-harmonics
Categories:33C50, 33C45, 42C10

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