Geodesic
Coefficients with respect to orthogonal-like decomposition systems
Sbornik. Mathematics, Tome 188 (1997) no. 12, pp. 1783-1798

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Properties of orthogonal-like decomposition systems are analyzed. It is shown in § 1 that such systems have most properties of orthogonal systems; the properties of the coefficients of the corresponding expansions are studied. A criterion enabling one to determine whether an orthogonal-like system is an orthogonal projection of an orthogonal system is established in § 2. In § 3 it is shown that Parseval's equality holds for a system satisfying certain natural conditions if and only if this is an orthogonal-like decomposition system. 
@article{SM_1997_188_12_a3,
     author = {T. P. Lukashenko},
     title = {Coefficients with respect to orthogonal-like decomposition  systems},
     journal = {Sbornik. Mathematics},
     pages = {1783--1798},
     publisher = {mathdoc},
     volume = {188},
     number = {12},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_12_a3/}
}
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T. P. Lukashenko. Coefficients with respect to orthogonal-like decomposition  systems. Sbornik. Mathematics, Tome 188 (1997) no. 12, pp. 1783-1798. http://geodesic.mathdoc.fr/item/SM_1997_188_12_a3/