Bounded Functions and Fourier Transforms

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jun 1958Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 9, page 440 (issn: 0002-9939,

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Authors: Edwards, R. E.;

doi: 10.2307/2033001 , 10.1090/s0002-9939-1958-0100203-5

Bounded Functions and Fourier Transforms

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Abstract

1. Statement of the principal result. The class of sequences obtainable as Fourier coefficients of measures on the circle group presents numerous structure problems of interest. Amongst the earliest results somewhat akin to that stated below appear Banach's theorems about lacunary coefficients; see e.g., [4, pp. 215-220]. More recently Helson [3] has studied analogous questions when the group concerned is the real line. The aim of the present paper is to give a simple proof by abstract methods of the following

Keywords

functional analysis

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