Growth properties of the Fourier transform

Abstract

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.

Document Type

Article

DOI

https://doi.org/10.2298/FIL1204755B

Keywords

Fourier transform, Helgason Fourier transform, Spherical means

Publication Date

11-1-2012

Journal Title

Filomat

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