Geodesic
A Fourier series in an arbitrary bounded orthonormal system that diverges on a set of positive measure
Sbornik. Mathematics, Tome 27 (1975) no. 3, pp. 393-405 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that every system of collectively bounded orthonormal functions admits an integrable function whose Fourier series diverges on a set of positive measure. Bibliography: 6 titles. 
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S. V. Bochkarev. A Fourier series in an arbitrary bounded orthonormal system that diverges on a set of positive measure. Sbornik. Mathematics, Tome 27 (1975) no. 3, pp. 393-405. http://geodesic.mathdoc.fr/item/SM_1975_27_3_a5/

[2] A. Zigmund, Trigonometricheskie ryady, t. 1, izd-vo «Mir», Moskva, 1965 | MR

[3] R. Paley, “A remarkable system of orthogonal functions”, Proc. London Math. Soc., 34 (1932), 241–279 | DOI | Zbl

[4] S. V. Bochkarev, “Ob absolyutnoi skhodimosti ryadov Fure po ogranichennym polnym ortonormirovannym sistemam”, Matem. sb., 93 (134) (1974), 203–217 | Zbl

[5] S. V. Bochkarev, Klassy funktsii i koeffitsienty Fure po polnym ortonormirovannym sistemam, Doktorskaya dissertatsiya, Moskva, 1974

[6] A. M. Olevskii, “Ryady Fure i funktsii Lebega”, Uspekhi matem. nauk, XXII:2 (134) (1967), 237–239 | MR