Journal of Fourier Analysis and Applications

, Volume 16, Issue 1, pp 34–51

Fourier Inversion of Distributions Supported by a Hypersurface

Article

DOI: 10.1007/s00041-009-9073-1

Cite this article as:
González Vieli, F.J. & Seifert, E. J Fourier Anal Appl (2010) 16: 34. doi:10.1007/s00041-009-9073-1

Abstract

Let μΣ be the natural measure on RN (N≥3) supported by a compact oriented analytic hypersurface Σ, ψ a smooth function on RN and P(D) a differential operator in N variables of order m. We determine a sufficient condition on the number λ such that the Fourier integral of the distribution P(D)ψμΣ be summable by Cesàro means of order λ to zero in a point outside the hypersurface. This condition depends on m and on the position of the point with respect to the caustic of the hypersurface.

Keywords

Fourier transformDistributionHypersurfaceCesàro means

Mathematics Subject Classification (2000)

42B1046F12

Copyright information

© Birkhäuser Boston 2009

Authors and Affiliations

  1. 1.LausanneSwitzerland
  2. 2.LausanneSwitzerland