Geodesic
On divergent Fourier series in orthogonal systems
Sbornik. Mathematics, Tome 22 (1974) no. 4, pp. 547-560 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this work there is constructed a complete orthonormal system with respect to which the Fourier series of piecewise continuous non-identically-zero functions diverge a.e. There is also constructed an orthonormal system with respect to which the Fourier series of continuous functions converge a.e., while the Fourier series of bounded functions having at least one discontinuity of the first kind diverge a.e. Bibliography: 10 titles. 
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     author = {A. S. Krantsberg},
     title = {On divergent {Fourier} series in orthogonal systems},
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A. S. Krantsberg. On divergent Fourier series in orthogonal systems. Sbornik. Mathematics, Tome 22 (1974) no. 4, pp. 547-560. http://geodesic.mathdoc.fr/item/SM_1974_22_4_a4/

[1] S. Kachmazh, G. Shteingauz, Teoriya ortogonalnykh ryadov, Fizmatgiz, Moskva, 1958

[2] S. Banach, “Sur la divergence des series orthogonales”, Studia Math., 9 (1940), 139–154 | MR

[3] P. L. Ulyanov, “Reshennye i nereshennye problemy teorii trigonometricheskikh i ortogonalnykh ryadov”, Uspekhi matem. nauk, XIX:1 (115) (1964), 3–69 | MR

[4] A. M. Olevskii, “Ob osobennostyakh tipa Karlemana dlya polnykh ortonormalnykh sistem”, Sib. matem. zh., 8:4 (1967), 807–826 | MR | Zbl

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

[6] A. M. Olevskii, “O prodolzhenii posledovatelnosti funktsii do polnoi ortonormirovannoi sistemy”, Matem. zametki, 6:6 (1969), 737–747 | MR | Zbl

[7] A. M. Olevskii, “Primer ortonormirovannoi sistemy skhodimosti v $C$, no ne v $L^2$”, Matem. sb., 91 (133) (1973), 134–141 | MR | Zbl

[8] V. F. Gaposhkin, “O skhodimosti ryadov po slabo multiplikativnym sistemam funktsii”, Matem. sb., 89 (131) (1972), 355–365 | Zbl

[9] E. M. Nikishin, P. L. Ulyanov, “Ob absolyutnoi i bezuslovnoi skhodimosti”, Uspekhi matem. nauk, XXII:3 (135) (1967), 240–242

[10] V. M. Veselov, “O sistemakh skhodimosti i raskhodimosti v prostranstvakh $C$ i $B$”, Matem. zametki, 13:6 (1973), 911–922 | MR | Zbl