Finite sums of products of functions in single variables. (English) Zbl 0714.26007

Author’s summary: A characterization is given of smooth functions H of k variables that admit decompositions into a finite sum of products of k functions of single variables only. This sufficient and necessary condition is given in terms of certain ordinary linear differential equations formed from a given H, which also serve for the construction of the functions in single variables occurring in such a decomposition. Conditions for the existence of special decompositions are also given, including the case of three variables when \(H(x,y,t)=\sum^{N}_{i=1}f_ i(x)g_ i(y)h_ i(t)\).
Reviewer: J.Rákosník


26B40 Representation and superposition of functions
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