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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

MSC:

26B40 Representation and superposition of functions
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References:

[1] Gauchman, H.; Rubel, L.A., Sums of products of functions of x times functions of y, Linear algebra appl., 125, 19-63, (1989) · Zbl 0695.26007
[2] Neuman, F., Functions of two variables and matrices involving factorizations, C.R. math. rep. acad. sci. Canada, 3, 7-11, (1981) · Zbl 0449.15009
[3] Neuman, F., Factorizations of matrices and functions of two variables, Czechoslovak math. J., 32, 582-588, (1982) · Zbl 0517.15012
[4] Neuman, F., Functions of the form \(∑\^{}\{N\}i = 1ƒi(x)gi(t)\) in L2, Arch. math. (Brno), 18, 19-22, (1982)
[5] Rassias, T.M., A criterion for a function to be represented as a sum of products of factors, Bull. inst. math. acad. sinica, 14, 337-382, (1986) · Zbl 0643.26009
[6] Rassias, T.M., Problem P286 in “problems and solutions” section, Aequationes math., 38, 111-112, (1989)
[7] Stéphanos, C., Sur une catégorie d’ équations functionnelles, Rend. circ. mat. Palermo, 18, 360-362, (1904) · JFM 35.0391.02
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