Summability of Fourier orthogonal series for Jacobi weight functions on the simplex in
Author:
Yuan Xu
Journal:
Proc. Amer. Math. Soc. 126 (1998), 3027-3036
MSC (1991):
Primary 33C50, 42C05, 41A63
DOI:
https://doi.org/10.1090/S0002-9939-98-04415-3
MathSciNet review:
1452834
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We study the Fourier expansion of a function in orthogonal polynomial series with respect to the weight functions
on the standard simplex in
. It is proved that such an expansion is uniformly
summable on the simplex for any continuous function if and only if
. Moreover, it is shown that
means define a positive linear polynomial identity, and the index is sharp in the sense that
means are not positive for
.
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Additional Information
Yuan Xu
Affiliation:
Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222
Email:
yuan@math.uoregon.edu
DOI:
https://doi.org/10.1090/S0002-9939-98-04415-3
Keywords:
Orthogonal polynomials in several variables,
on simplex,
Ces\`{a}ro summability,
positive kernel
Received by editor(s):
March 14, 1997
Additional Notes:
Supported by the National Science Foundation under Grant DMS-9500532.
Communicated by:
Palle E. T. Jorgensen
Article copyright:
© Copyright 1998
American Mathematical Society