Decomposable functions of several variables Martin Čadek Jaromir Šimša Research Papers Received: 13 April 1989 Revised: 15 January 1990 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 problem

P286 of these Aequationes, proposed also by

H. Gauchman and

L. A. Rubel in [3]. Necessary and sufficient conditions on

H 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

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Google Scholar Authors and Affiliations Martin Čadek Jaromir Šimša 1. Czechoslovak Academy of Sciences Mathematical Institute Brno Czechoslovakia