Geodesic
Absolute convergence of Fourier series over complete orthonormal systems of functions
Sbornik. Mathematics, Tome 14 (1971) no. 3, pp. 429-437 
S. V. Bochkarev. Absolute convergence of Fourier series over complete orthonormal systems of functions. Sbornik. Mathematics, Tome 14 (1971) no. 3, pp. 429-437. http://geodesic.mathdoc.fr/item/SM_1971_14_3_a7/
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     author = {S. V. Bochkarev},
     title = {Absolute convergence of {Fourier} series over complete orthonormal systems of functions},
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     year = {1971},
     volume = {14},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1971_14_3_a7/}
}
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In the paper results of the type of the Bernstein–Saks theorem and Carleman's singularity are established for arbitrary complete orthonormal systems, as well as for any countable family of such systems. The method of proof is based on utilizing series with random arrangement of signs. Bibliography: 5 titles.

[1] A. Zigmund, Trigonometricheskie ryady, t. 1, Mir, Moskva, 1965 | MR

[2] L. Ciesielski, “Properties of the orthonormal Franklin system”, Studia Math., 23 (1963), 141–157 | MR | Zbl

[3] S. V. Bochkarev, “O koeffitsientakh Fure funktsii klassa $\operatorname{Lip}\alpha$ po polnym ortonormirovannym sistemam”, Matem. zametki, 7:4 (1970), 397–402 | Zbl

[4] B. S. Mityagin, “Ob absolyutnoi skhodimosti ryada koeffitsientov Fure”, DAN SSSR, 157:5 (1964), 1047–1050 | Zbl

[5] A. M. Olevskii, “Raskhodyaschiesya ryady Fure”, Izv. AN SSSR, seriya matem., 27 (1963), 343–366 | MR | Zbl