Geodesic
On the representation of functions by series of Legandre polynomials in weighted $L_\mu^q [-1, 1]$ spaces
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2001), pp. 136-138 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we construct the weighted $L_\mu^q[-1, 1], q \in[1, 4/3] \cup [4, +\infty)$ and Legandre series $\sum\limits_{k=1}^\infty c_p P_k(x) $, which is universal in $L_\mu^q [-1, 1]$.
Keywords: functions by series of Legandre polynomials. 
@article{UZERU_2001_1_a5,
     author = {M. G. Grigoryan and A. S. Sarkisyan},
     title = {On the representation of functions by series of {Legandre} polynomials in weighted $L_\mu^q [-1, 1]$ spaces},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {136--138},
     year = {2001},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2001_1_a5/}
}
TY  - JOUR
AU  - M. G. Grigoryan
AU  - A. S. Sarkisyan
TI  - On the representation of functions by series of Legandre polynomials in weighted $L_\mu^q [-1, 1]$ spaces
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2001
SP  - 136
EP  - 138
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/UZERU_2001_1_a5/
LA  - ru
ID  - UZERU_2001_1_a5
ER  - 
%0 Journal Article
%A M. G. Grigoryan
%A A. S. Sarkisyan
%T On the representation of functions by series of Legandre polynomials in weighted $L_\mu^q [-1, 1]$ spaces
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2001
%P 136-138
%N 1
%U http://geodesic.mathdoc.fr/item/UZERU_2001_1_a5/
%G ru
%F UZERU_2001_1_a5
M. G. Grigoryan; A. S. Sarkisyan. On the representation of functions by series of Legandre polynomials in weighted $L_\mu^q [-1, 1]$ spaces. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2001), pp. 136-138. http://geodesic.mathdoc.fr/item/UZERU_2001_1_a5/

[1] A. A. Talalyan, “Predstavlenie izmerimykh funktsii ryadami”, Uspekhi mat. nauk, 15:5 (1969), 77–141

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

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

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

[5] M. G. Grigorian, “On the representation of functions by orthogonal series in weighted $L^p$ spaces”, Studia Math., 134:3 (1999), 207–216 | DOI | MR | Zbl