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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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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.

References [Enhancements On Off] (What's this?)

  • [BC] L. Brandolini and L. Colzani, Localization and convergence of eigenfunction expansions, J. Fourier Anal. 5 (1999), 431-447.
  • [D] J. J. Duistermaat, Fourier Integral Operators, Birkhäuser, Boston, 1996. MR 96m:58245
  • [PT] M. Pinsky and M. Taylor, Pointwise Fourier inversion: a wave equation approach, J. Fourier Anal. 3 (1997), 647-703. MR 99d:42019
  • [T] M. Taylor, Pointwise Fourier inversion on tori and other compact manifolds, J. Fourier Anal. 5 (1999), 449-463.

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Additional Information

Michael E. Taylor
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599

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

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