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Elsevier, Journal of Approximation Theory, 2(159), p. 167-179, 2009

DOI: 10.1016/j.jat.2009.01.002

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Cesàro means of Jacobi expansions on the parabolic biangle

Journal article published in 2008 by Wolfgang zu Castell, W. zu Castell ORCID, Frank Filbir, Yuan Xu
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

We Study Cesaro (C, delta) means for two-variable Jacobi polynomials on the parabolic biangle B = {(x(1), x(2)) is an element of R(2) : 0 <= x(1)(2) <= x(2) <= 1}. Using the product formula derived by Koornwinder and Schwartz for this polynomial system, the Cesaro operator can be interpreted as a convolution operator. We then show that the Cesaro (C, delta) means of the orthogonal expansion on the biangle are uniformly bounded if delta > alpha + beta + 1, alpha >= beta >= 0. Furthermore, for delta >= alpha + 2 beta + 3/2 the means define positive linear operators.