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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on summability of multiple Laguerre expansions


Author: Yuan Xu
Journal: Proc. Amer. Math. Soc. 128 (2000), 3571-3578
MSC (1991): Primary 42C05, 33C50, 41A63
Published electronically: June 7, 2000
MathSciNet review: 1778279
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Abstract: A simple structure of the multiple Laguerre polynomial expansions is used to study the Cesàro summability above the critical index for the convolution type Laguerre expansions. The multiple Laguerre polynomial expansion of an $\ell ^{1}$-radial function $f_{0}(\vert\mathbf x\vert)$ is shown to be an $\ell ^{1}$-radial function that coincides with the Laguerre polynomial expansion of $f_{0}$, which allows us to settle the problem of summability below the critical index for the $\ell ^{1}$-radial functions.


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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: http://dx.doi.org/10.1090/S0002-9939-00-05725-7
PII: S 0002-9939(00)05725-7
Keywords: Laguerre polynomials, several variables, summability
Received by editor(s): February 5, 1999
Published electronically: June 7, 2000
Additional Notes: This research was supported by the National Science Foundation under Grant DMS-9802265.
Communicated by: Hal L. Smith
Article copyright: © Copyright 2000 American Mathematical Society