Cesàro means of Jacobi expansions on the parabolic biangle |
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| Authors: | W zu Castell F Filbir Y Xu |
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| Institution: | aInstitute of Biomathematics and Biometry, Helmholtz Zentrum München, German Research Center for Environmental Health, Ingolstädter Landstraße 1, 85764 Neuherberg, Germany;bDepartment of Mathematics, University of Oregon, Eugene, OR 97403-1222, USA |
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| Abstract: | We study Cesàro (C,δ) means for two-variable Jacobi polynomials on the parabolic biangle  . 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) means of the orthogonal expansion on the biangle are uniformly bounded if δ>α+β+1, α≥β≥0. Furthermore, for  the means define positive linear operators. |
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| Keywords: | Orthogonal expansion Cesà ro summability Parabolic biangle Two-variable orthogonal polynomials Positive linear operators Convolution operators |
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