This article is cited in 4 papers

Series of a system ${\varphi(nx)}$

E. M. Nikishin

M. V. Lomonosov Moscow State University

Abstract: Several theorems on series of systems $\{\varphi(nx)\}$ are proved. It is shown, in particular, that there exists a continuous function $\varphi(x)$ such that a series of the system $\{\varphi(2^nx)\}$ with coefficients in $l_2$ does not converge in measure on $[0,1]$. This provides the answer to a problem raised by P. L. Ul'yanov.

UDC: 517.5

Received: 28.11.1968

 English version: Mathematical Notes, 1969, 5:5, 316–319

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