On the Sidon-Telyakovskii integrability class for cosine series

Abstract

Various reformulations of the classical Sidon integrability condition for cosine series are considered. Two apparent generalizations are shown to be equivalent to Sidon's condition. As an offshoot of these results it is shown that if the cosine Fourier coefficients satisfy n|Δan| = o(1) (n → ∞), then ∥Sn(f) -f ∥ = o(1) (n → ∞) is equivalent to anlg n = o(1) (n → ∞). © 1985.

Document Type

Article

DOI

https://doi.org/10.1016/0022-247X(85)90008-3

Publication Date

5-15-1985

Journal Title

Journal of Mathematical Analysis and Applications

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