aequationes mathematicae

, Volume 43, Issue 2–3, pp 248–263 | Cite as

The bestL2-approximation by finite sums of functions with separable variables

  • Jaromír Šimša
Research Papers


We consider the problem of the best approximation of a given functionh ∈ L2(X × Y) by sumsk=1nfkfk, with a prescribed numbern of products of arbitrary functionsfkL2(X) andgkL2(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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Copyright information

© Birkhäuser Verlag 1992

Authors and Affiliations

  • Jaromír Šimša
    • 1
  1. 1.Mathematical Institute of ČSAVBrnoCzechoslovakia

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