On convergence of certain cosine sums
Abstract: Rees and Stanojević introduced a new class of modified cosine sums and found a necessary and sufficient condition for integrability of these modified cosine sums. Here we show that to every classical cosine series with coefficients of bounded variation, a Rees-Stanojević cosine sum can be associated such that converges to pointwise, and a necessary and sufficient condition for convergence of to 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.
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-  Charles S. Rees and Caslav V. Stanojevic, Necessary and sufficient conditions for integrability of certain cosine sums, J. Math. Anal. Appl. 43 (1973), 579–586. MR 0322432, https://doi.org/10.1016/0022-247X(73)90278-3
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- C. S. Rees and Č. V. Stanojević, Necessary and sufficient conditions for integrability of certain cosine sums, J. Math. Anal. Appl. 43 (1973), 579-586. MR 48 #794. MR 0322432 (48:794)
- Č. V. Stanojević, On integrability of certain trigonometrical series, Srpska Akad. Nauka. Zb. Rad. 55 Mat. Inst. 6 (1957), 53-57. (Serbo-Croation) MR 20 #203. MR 0093680 (20:203)