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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Arithmetic means of Fourier coefficients


Author: Rajendra Sinha
Journal: Proc. Amer. Math. Soc. 55 (1976), 83-86
MSC: Primary 42A16
DOI: https://doi.org/10.1090/S0002-9939-1976-0397274-9
Addendum: Proc. Amer. Math. Soc. 60 (1976), 243-244.
MathSciNet review: 0397274
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Abstract: Given the Fourier coefficients of an even continuous function, we find a necessary and sufficient condition such that their arithmetic means are the Fourier coefficients of an odd continuous function. A similar result is shown for those Lipschitz classes whose elements are automatically equivalent to continuous functions.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0397274-9
Keywords: Fourier series, conjugate function, Lipschitz class, strong summability, closed graph theorem
Article copyright: © Copyright 1976 American Mathematical Society

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