Growth Properties of Fourier Transforms

Details Growth Properties of Fourier Transforms Growth Properties of Fourier Transforms

2009-10-06

arxiv.org/abs/0910.1115v2

Mathematics

Classical Analysis and ODEs

7 pages; undated version with a few details added and typos corrected

Scientific paper

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 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.

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