It is shown that to a certain cosine series f, a Rees-Stanojević cosine sumn can be associated such that gn converges to f pointwise, and a necessary and sufficient condition for L1 convergence of gn to f is given. As a corollary to that result we have a generalization of the classical result of this kind. Other corollaries are given concerning the well-known integrability conditions. © 1975, American Mathematical Society.
J. W. Garrett and C. V. Stanojevic, "On L¹ Convergence Of Certain Cosine Sums," Bulletin of the American Mathematical Society, vol. 82, no. 1, pp. 129 - 130, American Mathematical Society, Jan 1976.
The definitive version is available at https://doi.org/10.1090/S0002-9904-1976-13990-0
Mathematics and Statistics
Keywords and Phrases
Convergence of cosine sums; L 1
International Standard Serial Number (ISSN)
Article - Journal
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01 Jan 1976