caa a22 4500 465825354 CHVBK 20180323112147.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF02112277 doi (NATIONALLICENCE)springer-10.1007/BF02112277 Decomposable functions of several variables [Elektronische Daten] [Martin Čadek, Jaromir Šimša] 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. Birkhäuser Verlag, 1990 Primary 16B40 nationallicence Čadek Martin Czechoslovak Academy of Sciences, Mathematical Institute, Mendelova nám. 1, ČSR-603 00, Brno, Czechoslovakia aut Šimša Jaromir Czechoslovak Academy of Sciences, Mathematical Institute, Mendelova nám. 1, ČSR-603 00, Brno, Czechoslovakia aut aequationes mathematicae Birkhäuser-Verlag 40/1(1990-12-01), 8-25 0001-9054 40:1<8 1990 40 10 https://doi.org/10.1007/BF02112277 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02112277 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Čadek Martin Czechoslovak Academy of Sciences, Mathematical Institute, Mendelova nám. 1, ČSR-603 00, Brno, Czechoslovakia aut NATIONALLICENCE 700 1- Šimša Jaromir Czechoslovak Academy of Sciences, Mathematical Institute, Mendelova nám. 1, ČSR-603 00, Brno, Czechoslovakia aut NATIONALLICENCE 773 0- aequationes mathematicae Birkhäuser-Verlag 40/1(1990-12-01), 8-25 0001-9054 40:1<8 1990 40 10 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer