Regularly varying rates of decrease for moduli of continuity and Fourier transforms of functions on \({\mathbb{R}}^ d\)
type: Item
instance of: scholarly article
title: Regularly varying rates of decrease for moduli of continuity and Fourier transforms of functions on \({\mathbb{R}}^ d\)
zbMATH Open document ID: 0734.42006
DOI: 10.1016/0022-247X(91)90211-H
author: Daren B. H. Cline
published in: Journal of Mathematical Analysis and Applications
publication date: 1991-01-01T00:00:00Z
review text: The author describes the correspondence between the rates of decrease for various moduli of continuity of a function on \({\mathbb{R}}^ d\) and for the tail-integral of the function's Fourier transform. The rates of decrease are described in terms of the class \(RV_{-\alpha}\) (regularly varying functions with exp -\(\alpha\)) defined as the class of all measurable functions \(s: [0,\infty]\to [0,\infty]\) such that \(\forall w>0,\lim_{t\to \infty}(s(wt)/s(t))=w^{-\alpha}.\)
Mathematics Subject Classification ID: 42B10
Mathematics Subject Classification ID: 42B05
zbMATH DE Number: 4214662
zbMATH Keywords: rates of decrease
zbMATH Keywords: moduli of continuity
zbMATH Keywords: tail-integral
zbMATH Keywords: Fourier transform
zbMATH Keywords: regularly varying functions
reviewed by: D. C. Struppa
MaRDI profile type: Publication
cites work: Über den Stetigkeitsmodul von Fourier-Reihen mit monotonen Koeffizienten
cites work: Q3782200
cites work: Q3992980
cites work: Q3772676
cites work: Lipschitz Behavior and Integrability of Characteristic Functions
cites work: Abelian and Tauberian theorems relating the local behavior of an integrable function to the tail behavior of its Fourier transform
cites work: Q3733431
cites work: Q5633348
cites work: Fourier-Koeffizienten und Funktionenklassen
cites work: On the behaviour of the characteristic function of a probability distribution in the neighbourhood of the origin
cites work: Q5667036
cites work: Lipschitz Behavior and Characteristic Functions
cites work: Slowly varying functions and asymptotic behavior of a class of integral transforms. III
cites work: Approximation by Fourier sums of functions with slowly decreasing Fourier coefficients
cites work: COMPLEX FOURIER--BESSEL TRANSFORMS
cites work: Fourier transforms of Dini-Lipschitz functions
description: scientific article; zbMATH DE number 4214662