Journal ArticleDOI
Saturation on locally compact abelian groups
Bernd Dreseler,Walter Schempp +1 more
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In this paper, saturation theorems for approximation processes generated by families (μt)t > 0 of complex bounded Radon measures on G and operating on a submodule of the Banach module over the convolution algebra are established.Abstract:
Let G be an arbitrary locally compact abelian group. It is the purpose of the present paper to establish saturation theorems for approximation processes generated by families (μt)t > 0 of complex bounded Radon measures on G and operating on a submodule of the Banach module Lp(G), Lp(G), over the convolution algebra
. A basic tool is the Fourier transform method and, in the case p>1 for noncompact G, its interpretation in the context of the theory of quasimeasures on G.read more
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Journal ArticleDOI
Saturation on locally compact abelian groups: An extended theorem
Bernd Dreseler,Walter Schempp +1 more
TL;DR: In this paper, the saturation theorem on G was extended for approximation processes (It)t>0 acting on the submodule CP(G), p∈]1,+∞[, of the convolutionM1(G)-module LP(G).
Book ChapterDOI
Zur Theorie der Saturierten Approximationsverfahren auf Lokalkompakten Abelschen Gruppen
References
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Abstract Harmonic Analysis
Edwin Hewitt,Kenneth A. Ross +1 more
TL;DR: The first € price and the £ and $ price are net prices, subject to local VAT as discussed by the authors, and prices and other details are subject to change without notice. All errors and omissions excepted.
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Fourier analysis and approximation
Paul L. Butzer,Rolf J. Nessel +1 more
TL;DR: In this article, the authors propose a method for approximating by Singular Integrals of Periodic Functions using Fourier Transform Transform Transformions of Derivatives (FTDFs).
Journal ArticleDOI
Theory of Bessel potentials. I
Nachman Aronszajn,K. T. Smith +1 more
TL;DR: In this article, the conditions générales d'utilisation (http://www.numdam.org/conditions) are defined, i.e., Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
Book
An introduction to the theory of multipliers
TL;DR: In this article, the authors present a general theory of multipliers and derive derived algebras for Lp(G), Lq(G) as a dual space.