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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 Cesàro and Riesz means of Jacobi and Laguerre expansions


Author: Christopher Meaney
Journal: Proc. Amer. Math. Soc. 131 (2003), 3123-3128
MSC (2000): Primary 42C05, 33C45, 42C10
Published electronically: December 30, 2002
MathSciNet review: 1992852
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Abstract: We show that for $\delta$ below certain critical indices there are functions whose Jacobi or Laguerre expansions have almost everywhere divergent Cesàro and Riesz means of order $\delta$.


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Additional Information

Christopher Meaney
Affiliation: Department of Mathematics, Macquarie University, North Ryde, New South Wales 2109, Australia
Email: chrism@maths.mq.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06853-3
PII: S 0002-9939(02)06853-3
Keywords: Jacobi polynomial, Laguerre function, Ces\`aro mean, Riesz mean, Cantor-Lebesgue Theorem, uniform boundedness
Received by editor(s): February 26, 2002
Received by editor(s) in revised form: April 29, 2002
Published electronically: December 30, 2002
Communicated by: Andreas Seeger
Article copyright: © Copyright 2002 American Mathematical Society