Cesàro means of Jacobi expansions on the parabolic biangle - Mathematics > Classical Analysis and ODEsReport as inadecuate




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Abstract: We study Ces\`aro $C,\delta$ means for two-variable Jacobi polynomials onthe parabolic biangle $B=\{x 1,x 2\in{\mathbb R}^2:0\leq x 1^2\leq x 2\leq1\}$. Using the product formula derived by Koornwinder and Schwartz for thispolynomial system, the Ces\`aro operator can be interpreted as a convolutionoperator. We then show that the Ces\`aro $C,\delta$ means of the orthogonalexpansion on the biangle are uniformly bounded if $\delta>\alpha+\beta+1$,$\alpha-\frac 12\geq\beta\geq 0$. Furthermore, for$\delta\geq\alpha+2\beta+\frac 32$ the means define positive linear operators.



Author: Wolfgang zu Castell, Frank Filbir, Yuan Xu

Source: https://arxiv.org/



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