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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On the ideal of unconditionally convergent Fourier series in $ L\sb{p}\,(G)$


Author: Gregory F. Bachelis
Journal: Proc. Amer. Math. Soc. 27 (1971), 309-312
MSC: Primary 42.56; Secondary 46.00
MathSciNet review: 0271640
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Abstract: Let $ G$ be a compact abelian group. We consider the ideal of functions in $ {L_p}(G)$ with unconditionally convergent Fourier series in the $ {L_p}$ norm. This ideal is shown to coincide with the ``Derived algebra'' of Helgason. A characterization of this ideal is given when $ p$ is an even integer.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0271640-X
PII: S 0002-9939(1971)0271640-X
Keywords: Derived algebra, $ \Lambda (p)$ sets, multiplier, unconditionally convergent Fourier series
Article copyright: © Copyright 1971 American Mathematical Society