Some factorizations of matrix functions in several variables
Archivum mathematicum, Tome 28 (1992) no. 1-2, pp. 85-94
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 15A23, 15A54, 26B40
Keywords: separation of variables; matrix-valued functions; functional and differential equations for factorizable functions
@article{ARM_1992_28_1-2_a11,
     author = {\v{S}im\v{s}a, Jarom{\'\i}r},
     title = {Some factorizations of matrix functions in several variables},
     journal = {Archivum mathematicum},
     pages = {85--94},
     year = {1992},
     volume = {28},
     number = {1-2},
     mrnumber = {1201870},
     zbl = {0784.15006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1992_28_1-2_a11/}
}
TY  - JOUR
AU  - Šimša, Jaromír
TI  - Some factorizations of matrix functions in several variables
JO  - Archivum mathematicum
PY  - 1992
SP  - 85
EP  - 94
VL  - 28
IS  - 1-2
UR  - http://geodesic.mathdoc.fr/item/ARM_1992_28_1-2_a11/
LA  - en
ID  - ARM_1992_28_1-2_a11
ER  - 
%0 Journal Article
%A Šimša, Jaromír
%T Some factorizations of matrix functions in several variables
%J Archivum mathematicum
%D 1992
%P 85-94
%V 28
%N 1-2
%U http://geodesic.mathdoc.fr/item/ARM_1992_28_1-2_a11/
%G en
%F ARM_1992_28_1-2_a11
Šimša, Jaromír. Some factorizations of matrix functions in several variables. Archivum mathematicum, Tome 28 (1992) no. 1-2, pp. 85-94. http://geodesic.mathdoc.fr/item/ARM_1992_28_1-2_a11/

[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

[CS 2] Čadek M. and Šimša J.: Decomposition of smooth functions of two multidimensional variables. Czechoslovak Math. J. 41(116) (1991), 342-358. | MR

[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

[Neu 1] Neuman F.: Factorizations of matrices and functions of two variables. Czechoslovak Math. J. 32(107) (1982), 582-588. | MR | Zbl

[Neu 2] Neuman F.: Finite sums of products of functions in single variables. Linear Algebra Appl. 134 (1990), 153-164. | MR | Zbl

[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

[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 | Zbl

[St] Cyparissos Stéphanos M.: Sur une categorie d’équations fonctionelles. in Rend. Circ. Mat. Palermo 18 (1904), 360-362.