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A Strong Converse of the Wiener-Levy Theorem

Published online by Cambridge University Press:  20 November 2018

Walter Rudin
Walter Rudin*
Affiliation:
University of Wisconsin
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Extract

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Let A1 denote the class of all complex functions on the unit circle which are sums of absolutely convergent trigonometric series; that is to say, the class of all f of the form

Similarly, if 1 < p < ∞, let Ap be the class of all complex functions f on the circle whose Fourier coefficients

satisfy the condition

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 14 , 1962 , pp. 694 - 701
Copyright
Copyright © Canadian Mathematical Society 1962

References

1. Helson, H., J. P. Kahane, Y. Katznelson, and Rudin, W., The functions which operate on Fourier transforms, Acta Math., 102 (1959), 135–157.Google Scholar
2. Katznelson, Y., Sur le calcul symbolique dans quelques algèbres de Banach, Ann. Sri. Ecole Norm. Sup., 76 (1959), 83–124.Google Scholar
3. Zygmund, A., Trigonometric Series, 2nd ed., Cambridge (1959), I.Google Scholar