On properties of bases after their orthogonalization

V. M. Veselov


Abstract: We wish to determine which $L^p$ spaces have bases formed by orthogonalizing a sequence of functions $\{f_n\}$ that is a basis in $C(0,1)$. We show that the answer to this question depends on the sequence of functions $\{f_n\}$ and also on the method of orthogonalization.

UDC: 513.88

MSC: Primary 46B15; Secondary 41A50, 42A52

Received: 01.04.1970

 English version: Mathematics of the USSR-Izvestiya, 1970, 4:6, 1429–1446

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