Sine and cosine series in $L_\varphi$ classes
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2013), pp. 24-42.

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We study sine and cosine series with monotone with respect to subsequences coefficients. We establish conditions under which their sums belong to classes $L_\varphi$.
Keywords: monotonicity, series, subsequence
Mots-clés : coefficients.
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B. V. Simonov. Sine and cosine series in $L_\varphi$ classes. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2013), pp. 24-42. http://geodesic.mathdoc.fr/item/IVM_2013_10_a2/

[1] Bari N. K., Trigonometricheskie ryady, Fizmatgiz, M., 1961 | MR

[2] Vukolova T. M., Dyachenko M. I., “O svoistvakh summ trigonometricheskikh ryadov s monotonnymi koeffitsientami”, Vestn. Mosk. un-ta. Ser. 1. Matem. Mekhan., 1995, no. 3, 22–32 | MR | Zbl

[3] Zigmund A., Trigonometricheskie ryady, v. 1, Mir, M., 1965 | MR

[4] Bari N. K., Stechkin S. B., “Nailuchshie priblizheniya i differentsialnye svoistva dvukh sopryazhennykh funktsii”, Tr. Mosk. matem. o-va, 5, 1956, 483–522 | MR | Zbl

[5] Potapov M. K., Berisha M., “Moduli gladkosti i koeffitsienty Fure periodicheskikh funktsii”, Publ. inst. math., 26 (1979), 215–228 | MR | Zbl

[6] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1977 | MR