Growth properties of Fourier transforms via moduli of continuity

William O. Bray; Mark A. Pinsky

doi:10.1016/j.jfa.2008.06.017

Growth properties of Fourier transforms via moduli of continuity

William O. Bray^*, Mark A. Pinsky

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

42 Scopus citations

Abstract

We obtain new inequalities for the Fourier transform, both on Euclidean space, and on non-compact, rank one symmetric spaces. In both cases these are expressed as a gauge on the size of the transform in terms of a suitable integral modulus of continuity of the function. In all settings, the results present a natural corollary: a quantitative form of the Riemann-Lebesgue lemma. A prototype is given in one-dimensional Fourier analysis.

Original language	English (US)
Pages (from-to)	2265-2285
Number of pages	21
Journal	Journal of Functional Analysis
Volume	255
Issue number	9
DOIs	https://doi.org/10.1016/j.jfa.2008.06.017
State	Published - Nov 1 2008

Keywords

Bessel and Jacobi functions
Helgason Fourier transform
Spherical means
Symmetric space

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2008.06.017

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abstract = "We obtain new inequalities for the Fourier transform, both on Euclidean space, and on non-compact, rank one symmetric spaces. In both cases these are expressed as a gauge on the size of the transform in terms of a suitable integral modulus of continuity of the function. In all settings, the results present a natural corollary: a quantitative form of the Riemann-Lebesgue lemma. A prototype is given in one-dimensional Fourier analysis.",

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T1 - Growth properties of Fourier transforms via moduli of continuity

AU - Bray, William O.

AU - Pinsky, Mark A.

PY - 2008/11/1

Y1 - 2008/11/1

N2 - We obtain new inequalities for the Fourier transform, both on Euclidean space, and on non-compact, rank one symmetric spaces. In both cases these are expressed as a gauge on the size of the transform in terms of a suitable integral modulus of continuity of the function. In all settings, the results present a natural corollary: a quantitative form of the Riemann-Lebesgue lemma. A prototype is given in one-dimensional Fourier analysis.

AB - We obtain new inequalities for the Fourier transform, both on Euclidean space, and on non-compact, rank one symmetric spaces. In both cases these are expressed as a gauge on the size of the transform in terms of a suitable integral modulus of continuity of the function. In all settings, the results present a natural corollary: a quantitative form of the Riemann-Lebesgue lemma. A prototype is given in one-dimensional Fourier analysis.

KW - Bessel and Jacobi functions

KW - Helgason Fourier transform

KW - Spherical means

KW - Symmetric space

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DO - 10.1016/j.jfa.2008.06.017

M3 - Article

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SP - 2265

EP - 2285

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 9

ER -

Growth properties of Fourier transforms via moduli of continuity

Abstract

Keywords

ASJC Scopus subject areas

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