Abstract
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.
Recommended Citation
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
Department(s)
Mathematics and Statistics
Keywords and Phrases
L convergence of cosine sums 1
International Standard Serial Number (ISSN)
1088-6826; 0002-9939
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2023 American Mathematical Society, All rights reserved.
Publication Date
01 Jan 1976
