Growth properties of the Fourier transform

William O. Bray, Mark A. Pinsky

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


In a recent paper by the authors, growth properties of the Fourier transform on Euclidean space and the Helgason Fourier transform on rank one symmetric spaces of non-compact type were proved and expressed in terms of a modulus of continuity based on spherical means. The methodology employed first proved the result on Euclidean space and then, via a comparison estimate for spherical functions on rank one symmetric spaces to those on Euclidean space, we obtained the results on symmetric spaces. In this note, an analytically simple, yet overlooked refinement of our estimates for spherical Bessel functions is presented which provides significant improvement in the growth property estimates.

Original languageEnglish (US)
Pages (from-to)755-760
Number of pages6
Issue number4
StatePublished - Nov 2012


  • Fourier transform
  • Helgason Fourier transform
  • Spherical means

ASJC Scopus subject areas

  • General Mathematics


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