Journal of Fourier Analysis and Applications

, Volume 3, Issue 6, pp 647–703

Pointwise fourier inversion: A wave equation approach

  • Mark A. Pinsky
  • Michael E. Taylor
Article

DOI: 10.1007/BF02648262

Cite this article as:
Pinsky, M.A. & Taylor, M.E. The Journal of Fourier Analysis and Applications (1997) 3: 647. doi:10.1007/BF02648262

Abstract

Functions of the Laplace operator F(− Δ) can be synthesized from the solution operator to the wave equation. When F is the characteristic function of [0, R2], this gives a representation for radial Fourier inversion. A number of topics related to pointwise convergence or divergence of such inversion, as R → ∞, are studied in this article. In some cases, including analysis on Euclidean space, sphers, hyperbolic space, and certain other symmetric spaces, exact formulas for fundamental solutions to wave equations are available. In other cases, parametrices and other tools of microlocal analysis are effective.

Copyright information

© CRC Press LLC 1997

Authors and Affiliations

  • Mark A. Pinsky
    • 1
    • 2
  • Michael E. Taylor
    • 1
    • 2
  1. 1.Department of MathematicsNorthwestern UniversityEvanston
  2. 2.Department of MathematicsUniversity of North CarolinaChapel Hill