Rees and Stanojevic introduced a new class of modified cosine sums (equation omitted) and found a necessary and sufficient condition for integrability of these modified cosine sums. Here we show that to every classical cosine series f with coefficients of bounded variation, a Rees-Stanqjevic cosine sum gn can be associated such that gn converges to f pointwise, and a necessary and sufficient condition for Lx convergence of gn to f is given. As a corollary to that result we have a generalization of the classical result of this kind. Examples are given using the well-known integrability conditions. © 1976 American Mathematical Society.
J. W. Garrett and C. V. Stanojevic, "On L¹ Convergence Of Certain Cosine Sums," Proceedings of the American Mathematical Society, vol. 54, no. 1, pp. 101 - 105, American Mathematical Society, Jan 1976.
The definitive version is available at https://doi.org/10.1090/S0002-9939-1976-0394002-8
Mathematics and Statistics
Keywords and Phrases
L convergence of cosine sums 1
International Standard Serial Number (ISSN)
Article - Journal
© 2023 American Mathematical Society, All rights reserved.
01 Jan 1976