Cesàro means of Jacobi expansions on the parabolic biangle Original Research Article

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