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

 

On pointwise convergence of Fourier series
of radial functions in several variables


Author: Shigehiko Kuratsubo
Journal: Proc. Amer. Math. Soc. 127 (1999), 2987-2994
MSC (1991): Primary 42B05
Published electronically: April 28, 1999
MathSciNet review: 1605996
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove the pointwise convergence of the Fourier series for radial functions in several variables, which in the case $n=1$ is the Dirichlet-Jordan theorem itself. In our proof the method for the case of the indicator function of the ball is very useful.


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Additional Information

Shigehiko Kuratsubo
Affiliation: Department of Mathematics, Hirosaki University, Hirosaki 036, Japan
Email: kuratubo@cc.hirosaki-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04886-8
PII: S 0002-9939(99)04886-8
Keywords: Fourier series, spherical partial sum, bounded variation, indicator function, lattice point problem
Received by editor(s): September 30, 1997
Received by editor(s) in revised form: January 7, 1998
Published electronically: April 28, 1999
Communicated by: Frederick W. Gehring
Article copyright: © Copyright 1999 American Mathematical Society