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zu Castell, W. ; Filbir, F. ; Xu, Y.*

Cesàro means of Jacobi expansions on the parabolic biangle.

J. Approx. Theory 159, (Sp. Iss. SI), 167-179 (2009)
DOI
Open Access Green as soon as Postprint is submitted to ZB.
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.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Orthogonal expansion; Cesaro summability; Parabolic biangle; Two-variable orthogonal polynomials; Positive linear operators; Convolution operators; orthogonal polynomials
ISSN (print) / ISBN 0021-9045
e-ISSN 1096-0430
Journal Journal of Approximation Theory
Quellenangaben Volume: 159, Issue: 2, Pages: 167-179, Article Number: , Supplement: (Sp. Iss. SI)
Publisher Elsevier
Reviewing status Peer reviewed
Institute(s) Institute of Biomathematics and Biometry (IBB)