Divergent Laguerre series

We prove failure of a.e. convergence of partial sums of Laguerre expansions of L^{p} functions for p>4. The idea which is used goes back to Stanton and Tomas. We follow Meaney's paper (1983), where divergence results were proved in the Jacobi polynomial case.

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Bibliographic Details
Published in:	Proceedings of the American Mathematical Society Vol. 129; no. 4; pp. 1123 - 1126
Main Author:	Stempak, Krzysztof
Format:	Journal Article
Language:	English
Published:	American Mathematical Society 01-04-2001
Subjects:	Mathematical functions Mathematical inequalities Mathematical theorems Mathematics Partial sums Polynomials Series convergence divergence almost everywhere Laguerre polynomials and functions
Online Access:	Get full text
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Description
Summary:	We prove failure of a.e. convergence of partial sums of Laguerre expansions of L^{p} functions for p>4. The idea which is used goes back to Stanton and Tomas. We follow Meaney's paper (1983), where divergence results were proved in the Jacobi polynomial case.
ISSN:	0002-9939 1088-6826
DOI:	10.1090/S0002-9939-00-05657-4