Previous |  Up |  Next


separation of variables; matrix-valued functions; functional and differential equations for factorizable functions
We establish some criteria for a nonsingular square matrix depending on several parameters to be represented in the form of a matrix product of factors which depend on the single parameters.
[d’Al] d’Alembert J.: Recherches sur la courbe que forme une corde tendue mise en vibration I – II. Hist. Acad. Berlin (1747), 214-249.
[CS 1] Čadek M. and Šimša J.: Decomposable functions of several variables. Aequationes Math. 40 (1990), 8-25. MR 1055187
[CS 2] Čadek M. and Šimša J.: Decomposition of smooth functions of two multidimensional variables. Czechoslovak Math. J. 41(116) (1991), 342-358. MR 1105450
[GR] Gauchman H. and Rubel L. A.: Sums of products of functions of $x$ times functions of $y$. Linear Algebra Appl. 125 (1989), 19-63. MR 1024482
[Neu 1] Neuman F.: Factorizations of matrices and functions of two variables. Czechoslovak Math. J. 32(107) (1982), 582-588. MR 0682133 | Zbl 0517.15012
[Neu 2] Neuman F.: Finite sums of products of functions in single variables. Linear Algebra Appl. 134 (1990), 153-164. MR 1060018 | Zbl 0714.26007
[NR] Neuman F. and Rassias Th. M.: Functions decomposable into finite sums of products. in “Constantin Carathéodory: An International Tribute”, World Scientific Publ. Co., 1991, pp. 956-963. MR 1130873
[Ra] Rassias Th. M.: A criterion for a function to be represented as a sum of products of factors. Bull. Inst. Math. Acad. Sinica 14 (1986), 377-382. MR 0885367 | Zbl 0643.26009
[St] Cyparissos Stéphanos M.: Sur une categorie d’équations fonctionelles. in Rend. Circ. Mat. Palermo 18 (1904), 360-362.
Partner of
EuDML logo