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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
DOI: https://doi.org/10.1090/S0002-9939-00-05789-0
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.


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, Progress in Mathematics, vol. 130, Birkhäuser Boston, Inc., Boston, MA, 1996. MR 1362544
  • [PT] Mark A. Pinsky and Michael E. Taylor, Pointwise Fourier inversion: a wave equation approach, J. Fourier Anal. Appl. 3 (1997), no. 6, 647–703. MR 1481629, https://doi.org/10.1007/BF02648262
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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: https://doi.org/10.1090/S0002-9939-00-05789-0
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