A note on summability of multiple Laguerre expansions

Xu, Yuan

doi:10.1090/S0002-9939-00-05725-7

A note on summability of multiple Laguerre expansions
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Proc. Amer. Math. Soc. 128 (2000), 3571-3578 Request permission

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.

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