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Some notes on an expansion theorem of Paley and Wiener
1942
Bulletin of the American Mathematical Society
have formulated a criterion for a set of functions {g n } to be "near" a given orthonormal set {/ w }. The interest of this criterion is that it guarantees the set {g n } to have expansion properties similar to an orthonormal set. 2 In particular, they show that the set \g n ) approximately satisfies Parseval's formula. In the first part of this paper we show that, conversely, if a set {g n } approximately satisfies Parseval's formula then there exists at least one orthonormal set which it is
doi:10.1090/s0002-9904-1942-07797-4
fatcat:cf4b2u4jebhjbkgfdiv3gn3hwu