Cesàro means of Jacobi expansions on the parabolic biangle

Castell, Wolfgang zu; Filbir, Frank; Xu, Yuan

Cesàro means of Jacobi expansions on the parabolic biangle

Authors

Castell, Wolfgang zu

Filbir, Frank

Xu, Yuan

Description

We study Cesàro $(C,δ)$ means for two-variable Jacobi polynomials on the parabolic biangle $B=\{(x_1,x_2)\in{\mathbb R}^2:0\leq x_1^2\leq x_2\leq 1\}$. 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 $δ>α+β+1$, $α-\frac 12\geqβ\geq 0$. Furthermore, for $δ\geqα+2β+\frac 32$ the means define positive linear operators.