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Some estimates of the rate of summability of orthogonal series by linear means

A. V. Efimov

Moscow Institute of Electronic Engineering

Abstract: An estimate of the rate of convergence of linear means of the orthogonal series of an $L^2$ function $f(x)$ generated by a summation function is established. This estimate depends on the rate of growth of factors which do not destroy the convergence of the series of squares of coefficients of $f(x)$ with respect to the orthonormal system under consideration.

UDC: 517.5

Received: 08.01.1968

 English version: Mathematical Notes, 1968, 4:3, 650–654

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