Systems of functions which are complete in measure

N. B. Pogosyan

M. V. Lomonosov Moscow State University

Abstract: In this note it is proved that if a complete orthonormal system $\{\varphi_n\}$ in $L_2[0,1]$ contains a subsystem $\{\varphi_{n_k}\}$ of a lacunary order $p>2$, then for some bounded measurable function $h(x)$ the system $\{h(x)\varphi_n(x)\}_{n\ne n_k}$ is complete in $L_2[0,1]$.

UDC: 517.5

Received: 19.05.1975

 English version: Mathematical Notes, 1975, 18:6, 1075–1080

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