On the order of partial sums of general orthogonal series.

Autor: Davtyan, R.
Zdroj: Mathematical Notes; Oct1969, Vol. 6 Issue 4, p725-732, 8p
Abstrakt: It is shown that for convergence of every orthonormal system ϕ( 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 $$\sum\nolimits_{n = 1}^\infty {a_n^2 = + \infty } $$ there hold $$\sum\nolimits_{n = 1}^\infty {a_n^2 = + \infty } $$ almost everywhere on [0, 1]. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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