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

 

Pointwise Fourier inversion--An addendum


Author: Michael E. Taylor
Journal: Proc. Amer. Math. Soc. 129 (2001), 2001-2003
MSC (2000): Primary 42B08, 35P10
Published electronically: November 21, 2000
MathSciNet review: 1825908
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Abstract:

In this note we complete a circle of results presented in §5 of an earlier work of the author (J. Fourier Anal. 5 (1999), 449-463), establishing the endpoint case of Proposition 10 of that paper. As a consequence, we have results on pointwise convergence of the Fourier series (summed by spheres) of a function on the 3-dimensional torus with a simple jump across a smooth surface $\Sigma$, with no curvature hypotheses on $\Sigma$, extending Proposition 7 of that paper.


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Additional Information

Michael E. Taylor
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599
Email: met@math.unc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05789-0
PII: S 0002-9939(00)05789-0
Keywords: Fourier series
Received by editor(s): October 20, 1999
Published electronically: November 21, 2000
Additional Notes: The author was partially supported by NSF grant DMS-9877077
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2000 American Mathematical Society