On the Sidon-Telyakovskii integrability class for cosine series
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.
Bray, William O. "On the Sidon-Telyakovskii integrability class for cosine series." Journal of mathematical analysis and applications 108, no. 1 (1985): 73-78.
Journal of Mathematical Analysis and Applications