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.
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Dreseler, B., Schempp, W. Saturation on locally compact abelian groups. Manuscripta Math 7, 141–174 (1972). https://doi.org/10.1007/BF01679710
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DOI: https://doi.org/10.1007/BF01679710