On the order of partial sums of general orthogonal series期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On the order of partial sums of general orthogonal series

Authors:	R. S. Davtyan

Affiliation:	(1) Institute of Mathematics and Mechanics, Academy of Sciences of the Armenian SSR, USSR

Abstract:	It is shown that for convergence of every orthonormal system_n(x) given on [0, l],it is necessary and sufficient that, under the condition $int_0^infty {tfrac{1}{{W^2 (x)}}dx< + infty }$ on tlie increasing function W(x) and for $sumnolimits_{n = 1}^infty {a_n^2 = + infty }$ there hold $sumnolimits_{n = 1}^infty {a_n^2 = + infty }$ almost everywhere on [0, 1].Translated from Matematicheskie Zametki, Vol. 6, No. 4, pp. 451–462, October, 1969.

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