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 | References | Similar Articles | Additional Information

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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Additional Information

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