Summability of orthogonal expansions of several variables.

DOI10.1016/S0021-9045(03)00069-8zbMath1041.42024OpenAlexW1993736459MaRDI QIDQ1395811

Yuan Xu, Zhongkai Li

Publication date: 1 July 2003

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0021-9045(03)00069-8

zbMATH Keywords

Cesàro summabilitysummabilityunit spheregeneralized Gegenbauer expansionsspherical \(h\)-harmonics

Mathematics Subject Classification ID

General harmonic expansions, frames (42C15)

Related Items (11)

Riesz transforms and fractional integration for orthogonal expansions on spheres, balls and simplices ⋮ Divergence of Cesàro means of spherical \(h\)-harmonic expansions ⋮ Maximal estimates for the Cesàro means of weighted orthogonal polynomial expansions on the unit sphere ⋮ Sharp estimates of the Cesàro kernels for weighted orthogonal polynomial expansions in several variables ⋮ Multivariate polynomial inequalities with respect to doubling weights and \(A_{\infty}\) weights ⋮ Generalized translation operator and approximation in several variables ⋮ Maximal function and multiplier theorem for weighted space on the unit sphere ⋮ Cesàro means of orthogonal expansions in several variables ⋮ Boundedness of projection operators and Cesàro means in weighted 𝐿^{𝑝} space on the unit sphere ⋮ Intertwining operator associated to symmetric groups and summability on the unit sphere ⋮ Cesàro means of Jacobi expansions on the parabolic biangle

Cites Work

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• Summability of product Jacobi expansions
• Orthogonal polynomials and summability in Fourier orthogonal series on spheres and on balls
• Differential-Difference Operators Associated to Reflection Groups
• The Product Formula and Convolution Structure for the Generalized Chebyshev Polynomials
• Integral Kernels with Reflection Group Invariance
• Weak type estimates for Cesàro sums of Jacobi polynomial series
• Summability of Fourier orthogonal series for Jacobi weight functions on the simplex in ℝ^{𝕕}
• Summability of Fourier orthogonal series for Jacobi weight on a ball in ℝ^{𝕕}
• Orthogonal Polynomials for a Family of Product Weight Functions on the Spheres
• Integration of the intertwining operator for $h$-harmonic polynomials associated to reflection groups
• Orthogonal Polynomials and Cubature Formulae on Spheres and on Balls
• Sommes De Cesaro Et Multiplicateurs Des Developpements en Harmoniques Spheriques

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