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

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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