| Title:
|
Some factorizations of matrix functions in several variables (English) |
| Author:
|
Šimša, Jaromír |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
28 |
| Issue:
|
1 |
| Year:
|
1992 |
| Pages:
|
85-94 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
separation of variables |
| Keyword:
|
matrix-valued functions |
| Keyword:
|
functional and differential equations for factorizable functions |
| MSC:
|
15A23 |
| MSC:
|
15A54 |
| MSC:
|
26B40 |
| idZBL:
|
Zbl 0784.15006 |
| idMR:
|
MR1201870 |
| . |
| Date available:
|
2008-06-06T21:05:00Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107440 |
| . |
| Reference:
|
[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. |
| Reference:
|
[CS 1] Čadek M. and Šimša J.: Decomposable functions of several variables.Aequationes Math. 40 (1990), 8-25. MR 1055187 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[Neu 1] Neuman F.: Factorizations of matrices and functions of two variables.Czechoslovak Math. J. 32(107) (1982), 582-588. Zbl 0517.15012, MR 0682133 |
| Reference:
|
[Neu 2] Neuman F.: Finite sums of products of functions in single variables.Linear Algebra Appl. 134 (1990), 153-164. Zbl 0714.26007, MR 1060018 |
| Reference:
|
[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 |
| Reference:
|
[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. Zbl 0643.26009, MR 0885367 |
| Reference:
|
[St] Cyparissos Stéphanos M.: Sur une categorie d’équations fonctionelles.in Rend. Circ. Mat. Palermo 18 (1904), 360-362. |
| . |
