Cesàro means of Jacobi expansions on the parabolic biangle

2008/05/20 by Wolfgang zu Castell, Castell, Wolfgang zu, Frank Filbir +3
Mathematics · Physics and Astronomy · #33C50 #42C10 #Advanced Algebra and Geometry #Advanced Differential Geometry Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.0805.3026

openalex publication_date 2008/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Cesàro (C,δ) means for two-variable Jacobi polynomials on the parabolic biangle B=\(x₁,x₂)∈\mathbb R²:0≤ x₁²≤ x₂≤ 1\. Using the product formula derived by Koornwinder & Schwartz for this polynomial system, the Cesàro operator can be interpreted as a convolution operator. We then show that the Cesàro (C,δ) means of the orthogonal expansion on the biangle are uniformly bounded if δ>α+β+1, α-\frac 12≥β≥ 0. Furthermore, for δ≥α+2β+\frac 32 the means define positive linear operators.

Related

• Cesàro means of orthogonal expansions in several variables
• Divergent Cesaro and Riesz means of Jacobi and Laguerre expansions
• Fourier orthogonal series on a paraboloid
• Strong convergence theorem of Cesàro means with respect to the Walsh system
• Mixed norm estimates for the Cesàro means associated with Dunkl--Hermite expansions