Geodesic
On exact Weyl multipliers
Sbornik. Mathematics, Tome 36 (1980) no. 1, pp. 101-110 Cet article a éte moissonné depuis la source Math-Net.Ru

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The existence of a complete orthonormal system which has no exact Weyl multiplier is proved. It is shown that by rearrangements of the orthonormal system of D. E. Men'shov one can realize all exact Weyl multipliers, while the class of convex sequences is not large enough to contain all Weyl multipliers. Bibliography: 8 titles. 
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S. N. Poleshchuk. On exact Weyl multipliers. Sbornik. Mathematics, Tome 36 (1980) no. 1, pp. 101-110. http://geodesic.mathdoc.fr/item/SM_1980_36_1_a6/

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

[3] D. E. Menshov, “Sur les serie de fonctions orthogonales. I”, Fundam. Math., 4 (1923), 82–105

[4] A. A. Talalyan, “O skhodimosti ortogonalnykh ryadov”, DAN SSSR, 110:4 (1956), 515–516 | MR

[5] K. Tandori, “Über die orthogonalen Funktionen. V (Genaue Weylshe Multiplikatorfolgen)”, Acta Sci. Math. Szeged, 20:1 (1959), 1–13 | MR | Zbl

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

[7] V. Feller, Vvedenie v teoriyu veroyatnostei i ee primeneniya, izd-vo “Mir”, Moskva, 1967

[8] E. M. Nikishin, “Mnozhiteli Veilya dlya kratnykh ryadov Fure”, Matem. sb., 89(131) (1972), 340–348 | Zbl