A note on summability of multiple Laguerre expansions
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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 $f_{0}(|\mathbf x|)$ 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.References
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Additional Information
- Yuan Xu
- Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222
- MR Author ID: 227532
- Email: yuan@math.uoregon.edu
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 3571-3578
- MSC (1991): Primary 42C05, 33C50, 41A63
- DOI: https://doi.org/10.1090/S0002-9939-00-05725-7
- MathSciNet review: 1778279