aequationes mathematicae

, Volume 40, Issue 1, pp 8–25

Decomposable functions of several variables

  • Martin Čadek
  • Jaromir Šimša
Research Papers

DOI: 10.1007/BF02112277

Cite this article as:
Čadek, M. & Šimša, J. Aeq. Math. (1990) 40: 8. doi:10.1007/BF02112277

Summary

The paper deals with the functions which admit the decomposition
$$H(x,y,z) = \sum\limits_{i = 1}^m {f_i (x)\varphi _i (y,z)}$$
or
$$H(x,y,z) = \sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {\sum\limits_{k = 1}^p {\alpha _{ijk} f_i (x)g_j (y)h_k (z)} } }$$
and so it solves the problemP286 of these Aequationes, proposed also byH. Gauchman andL. A. Rubel in [3]. Necessary and sufficient conditions onH to have such a decomposition are formulated both for differentiable functions in terms of partial derivatives and for functions without any regularity assumptions. Many of these results can be extended to the case of more than three variables.

AMS (1980) subject classification

Primary 16B40 

Copyright information

© Birkhäuser Verlag 1990

Authors and Affiliations

  • Martin Čadek
    • 1
  • Jaromir Šimša
    • 1
  1. 1.Czechoslovak Academy of SciencesMathematical InstituteBrnoCzechoslovakia

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