The representation of measurable functions by usual and multiple series of Legendre polynomials
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (1988), pp. 143-146.

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The problem of representation of arbitrary functions by nstial and multiple series of Legendre polynomials in the sense of convergence in almost everywhere is considered in the paper.
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M. G. Grigoryan. The representation of measurable functions by usual and multiple series of Legendre polynomials. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (1988), pp. 143-146. http://geodesic.mathdoc.fr/item/UZERU_1988_1_a12/

[1] D. E. Menshov, “Sur la série de Fourier des fonctions continues”, Matem. sb., 8(50) (1940), 493–518 | MR

[2] D. E. Menshov, “Sur la représentation des fonctions mesurables par des séries trigonométrique”, Matem. sb., 9 (1941), 667–692 | MR | Zbl

[3] D. E. Menshov, “O ryadakh Fure ot summiruemykh funktsii”, Tr. Mosk. matem. ob-va, 1, 1952, 5–58 | MR | Zbl

[4] A. A. Talalyan, “Predstavlenie izmerimykh funktsii ryadami”, Uspekhi mat. nauk, 15:5 (1960), 77–141 | DOI | MR | Zbl

[5] P. L. Ulyanov, “Predstavlenie funktsii ryadami i klassy $\varphi(L)$”, UMN, 27:2 (1972), 3–52 | MR | Zbl

[6] M. G. Grigoryan, “O skhodimosti pochti vsyudu dvoinykh ryadov Fure summiruemykh funktsii”, Anal. Math., 11:3 (1985), 201–216 | DOI | MR | Zbl

[7] E. V. Gobson, Teoriya sfericheskikh i ellipsoidalnykh funktsii, IL, M., 1952

[8] H. Pollard, “The mean convergence of orthogonal series. III”, Duke Math. J., 16:1 (1949), 189–191 | DOI | MR | Zbl

[9] J. Neuman, W. Rudin, “Mean convergence of orthogonal series”, Proc. Amer. Math. Soc., 3 (1952), 219–222 | DOI | MR | Zbl

[10] K. S. Kazaryan, “O nekotorykh voprosakh teorii ortogonalnykh ryadov”, Matem. sb., 1982, no. 2, 278–294 | MR | Zbl

[11] B. S. Kashin, “Ob odnoi polnoi ortonormirovannoi sisteme”, Matem. sb., 99(141) (1976), 356–365 | MR | Zbl

[12] M. G. Grigoryan, “O skhodimosti v metrike LP i pochti vsyudu podposledovatelnostei sfericheskikh chastichnykh summ dvoinykh ryadov Fure po polnym ortonormirovannym sistemam”, Mezhvuzovskii sb. (Matematika), 1984, no. 2

[13] M. G. Grigoryan, “O skhodimosti sfericheskikh srednikh Rissa kratnykh integralov Fure”, DAN Arm. SSR, 69:2 (1979)