Pointwise Fourier inversion—An addendum
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- by Michael E. Taylor PDF
- Proc. Amer. Math. Soc. 129 (2001), 2001-2003 Request permission
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
- L. Brandolini and L. Colzani, Localization and convergence of eigenfunction expansions, J. Fourier Anal. 5 (1999), 431–447.
- J. J. Duistermaat, Fourier integral operators, Progress in Mathematics, vol. 130, Birkhäuser Boston, Inc., Boston, MA, 1996. MR 1362544
- 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, DOI 10.1007/BF02648262
- M. Taylor, Pointwise Fourier inversion on tori and other compact manifolds, J. Fourier Anal. 5 (1999), 449–463.
Additional Information
- Michael E. Taylor
- Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599
- MR Author ID: 210423
- Email: met@math.unc.edu
- 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
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1825908