aequationes mathematicae

, Volume 43, Issue 2, pp 248–263

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

  • Jaromír Šimša
Research Papers

DOI: 10.1007/BF01835707

Cite this article as:
Šimša, J. Aeq. Math. (1992) 43: 248. doi:10.1007/BF01835707


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)


Copyright information

© Birkhäuser Verlag 1992

Authors and Affiliations

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