Pointwise Fourier Inversion: A Wave Equation Approach

Mark A. Pinsky*, Michael E. Taylor

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

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, spheres, 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.

Original languageEnglish (US)
Pages (from-to)647-703
Number of pages57
JournalJournal of Fourier Analysis and Applications
Volume3
Issue number6
DOIs
StatePublished - 1997

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Applied Mathematics

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