Research Papers

aequationes mathematicae

, Volume 43, Issue 2, pp 248-263

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

  • Jaromír ŠimšaAffiliated withMathematical Institute of ČSAV

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Summary

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).

AMS (1980) subject classification (1985 revision)

41A50 41A30 46E30 45P05