Geodesic
On the extension of a sequence of functions to a complete orthonormal system
Matematičeskie zametki, Tome 6 (1969) no. 6, pp. 737-747 Cet article a éte moissonné depuis la source Math-Net.Ru

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Necessary and sufficient conditions for extending a sequence of functions to a complete orthonormal system on a larger set are indicated. As an application of the extension problem, a description of the space of coefficients of orthogonal series in a complete bounded system, converging on sets of positive measure, is given. 
@article{MZM_1969_6_6_a9,
     author = {A. M. Olevskii},
     title = {On the extension of a~sequence of functions to a~complete orthonormal system},
     journal = {Matemati\v{c}eskie zametki},
     pages = {737--747},
     year = {1969},
     volume = {6},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_6_6_a9/}
}
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A. M. Olevskii. On the extension of a sequence of functions to a complete orthonormal system. Matematičeskie zametki, Tome 6 (1969) no. 6, pp. 737-747. http://geodesic.mathdoc.fr/item/MZM_1969_6_6_a9/