Geodesic
Series in the system $\{f(nx)\}_{n=1}^\infty$
Izvestiya. Mathematics , Tome 27 (1986) no. 1, pp. 101-113.

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This article studies questions of convergence of operators commuting with ergodic endomorphisms, as well as convergence of function series of the form $\sum a_nf(nx)$, where $\{n\}_{n=1}^\infty$ is the sequence of positive integers, $x\in[0,1]$, and $f(x+1)=f(x)$, and series of the form $\sum a_nf(\tau^nx)$, where $\tau$ is an ergodic endomorphism of some algebra $G$, and $f\in L_2(G)$. Bibliography: 13 titles. 
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A. V. Kasyanchuk. Series in the system $\{f(nx)\}_{n=1}^\infty$. Izvestiya. Mathematics , Tome 27 (1986) no. 1, pp. 101-113. http://geodesic.mathdoc.fr/item/IM2_1986_27_1_a5/

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

[2] Zigmund A., Trigonometricheskie ryady, t. I, Mir, M., 1965 | MR

[3] Stein I., Veis G., Vvedenie v garmonicheskii analiz na evklidovykh prostranstvakh, Mir, M., 1974 | MR | Zbl

[4] Kornfeld I. P., Sinai Ya. G., Fomin S. V., Ergodicheskaya teoriya, Nauka, M., 1980 | MR

[5] Nikishin E. M., “O sistemakh skhodimosti”, Matem. sb., 81(123):1 (1970), 23–38 | Zbl

[6] Gaposhkin V. F., “O sistemakh vida $\{\varphi(nx)\}$, blizkikh k trigonometricheskoi sisteme”, Matem. sb., 51(93):2 (1960), 239–252 | Zbl

[7] Olevskii A. M., “Raskhodyaschiesya ryady Fure nepreryvnykh funktsii”, Dokl. AN SSSR, 141:1 (1961), 28–31 | MR | Zbl

[8] Orlicz W., “Über die unabhängig von Anordnung fast überall konvergenten Funktionenreihen”, Bull. de l'Acad. Polonaise, 1927, 117–125 | Zbl

[9] Toeplitz O., “Zur Theorie der Dirichletschen Reihen”, Amer. J. Math., 60 (1938), 880–888 | DOI | MR | Zbl

[10] Wintner A., “Diophantine approximations and Hilbert space”, Amer. J. Math., 66 (1944), 564–578 | DOI | MR | Zbl

[11] Marstrand J. M., “On Khinchin's conjecture about strong uniform distribution”, Proce London Math. Soc., ser. 3, 21 (1970), 540–556 | DOI | MR | Zbl

[12] Rosenblatt J., “Convergence of series of translations”, Math. Ann., 230 (1977), 245–272 | DOI | MR | Zbl

[13] Carleson L., “On convergence and growth of partial sums of Fourier series”, Acta Math., 116:1–2 (1966), 135–157 | DOI | MR | Zbl