The bestL2-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 ∈ L2(X × Y) by sums∑k=1nfkfk, with a prescribed numbern of products of arbitrary functionsfk ∈L2(X) andgk ∈L2(Y). As a co-product we develop a new proof of the Hilbert—Schmidt decomposition theorem for functions lying inL2(X × Y).
AMS (1980) subject classification (1985 revision)41A50 41A30 46E30 45P05
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