Geodesic
On properties of bases after their orthogonalization
Izvestiya. Mathematics , Tome 4 (1970) no. 6, pp. 1429-1446

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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. 
@article{IM2_1970_4_6_a8,
     author = {V. M. Veselov},
     title = {On properties of bases after their orthogonalization},
     journal = {Izvestiya. Mathematics },
     pages = {1429--1446},
     publisher = {mathdoc},
     volume = {4},
     number = {6},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1970_4_6_a8/}
}
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V. M. Veselov. On properties of bases after their orthogonalization. Izvestiya. Mathematics , Tome 4 (1970) no. 6, pp. 1429-1446. http://geodesic.mathdoc.fr/item/IM2_1970_4_6_a8/