Summary
We consider the problem of the best approximation of a given functionh ∈ L 2 (X × Y) by sums∑ nk=1 f k f k, with a prescribed numbern of products of arbitrary functionsf k ∈L 2 (X) andg k ∈L 2 (Y). As a co-product we develop a new proof of the Hilbert—Schmidt decomposition theorem for functions lying inL 2 (X × Y).
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Šimša, J. The bestL 2-approximation by finite sums of functions with separable variables. Aeq. Math. 43, 248–263 (1992). https://doi.org/10.1007/BF01835707
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DOI: https://doi.org/10.1007/BF01835707