, Volume 43, Issue 2-3, pp 248-263

The bestL 2-approximation by finite sums of functions with separable variables

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We consider the problem of the best approximation of a given functionh ∈ L 2 (X × Y) by sums k=1 n f k f k, with a prescribed numbern of products of arbitrary functionsf kL 2 (X) andg kL 2 (Y). As a co-product we develop a new proof of the Hilbert—Schmidt decomposition theorem for functions lying inL 2 (X × Y).