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


Divergent Laguerre series

Author: Krzysztof Stempak
Journal: Proc. Amer. Math. Soc. 129 (2001), 1123-1126
MSC (1991): Primary 42C10; Secondary 42C99
Published electronically: October 16, 2000
MathSciNet review: 1709766
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Abstract: 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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Krzysztof Stempak
Affiliation: Instytut Matematyczny Politechniki Wrocławskiej, Wyb. Wyspianskiego 27, 50-370 Wrocław, Poland

PII: S 0002-9939(00)05657-4
Keywords: Laguerre polynomials and functions, divergence almost everywhere
Received by editor(s): March 19, 1999
Received by editor(s) in revised form: July 2, 1999
Published electronically: October 16, 2000
Additional Notes: This research was supported in part by KBN grant # 2 PO3A 048 and European Commission via the TMR network “Harmonic Analysis”, contract no. ERB FMRX-CT970159.
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2000 American Mathematical Society