| Title:
|
On quadratic Hurwitz forms. I (English) |
| Author:
|
Gregor, Jiří |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
26 |
| Issue:
|
2 |
| Year:
|
1981 |
| Pages:
|
142-153 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
Homogeneous quadratic polynomials $f$ in $n$ complex variables are investigated and various necessary and sufficient conditions are given for $f$ to be nonzero in the set $\Gamma^{(n)}=\left\{z\in C^{(n)}:\text Re \ z>0\right\}$. Conclusions for the theory of multivariable positive real functions are formulated with applications in multivariable electrical network theory. (English) |
| Keyword:
|
Hurwitz polynomial |
| Keyword:
|
electrical networks |
| MSC:
|
15A63 |
| MSC:
|
93D20 |
| MSC:
|
94C05 |
| MSC:
|
94C99 |
| idZBL:
|
Zbl 0457.15016 |
| idMR:
|
MR0612670 |
| DOI:
|
10.21136/AM.1981.103904 |
| . |
| Date available:
|
2008-05-20T18:16:37Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103904 |
| . |
| Reference:
|
[1] N. K. Bose: Problems and Progress in Multidimensional Systems Theory.Proc. IEEE, Vol. 65, No. 6, June 1977, pp. 824-840. |
| Reference:
|
[2] M. Fiedler: .Private communication, 1979. Zbl 0431.15005 |
| Reference:
|
[3] J. Gregor: Multivariable positive real functions.Res. Rep. III-3-1/3, 1978 (in Czech). |
| Reference:
|
[4] T. Kоgа: Synthesis of finite passive N-ports with prescribed positive real matrices of several variables.IEEE Trans, on Circuit Th., Vol. CT-15, No. 1, March 1968, pp. 2-23. 10.1109/TCT.1968.1082780 |
| Reference:
|
[5] M. A. Lavrentyev B. V. Shabat: Methods of the Theory of Functions of a Complex Variable.(in Russian). FIZMATGIZ, Moscow 1958. |
| . |
