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

58 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

Access to Document

10.1016/j.jfa.2008.06.017

Cite this

@article{68b9ecfc3fef46c6ba808a8989fd7cc7,

title = "Growth properties of Fourier transforms via moduli of continuity",

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.",

keywords = "Bessel and Jacobi functions, Helgason Fourier transform, Spherical means, Symmetric space",

author = "Bray, {William O.} and Pinsky, {Mark A.}",

year = "2008",

month = nov,

day = "1",

doi = "10.1016/j.jfa.2008.06.017",

language = "English (US)",

volume = "255",

pages = "2265--2285",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "9",

}

TY - JOUR

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

UR - http://www.scopus.com/inward/record.url?scp=58049152965&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58049152965&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2008.06.017

DO - 10.1016/j.jfa.2008.06.017

M3 - Article

AN - SCOPUS:58049152965

SN - 0022-1236

VL - 255

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

Access to Document

Other files and links

Fingerprint

Cite this