Title:

On quadratic Hurwitz forms. I (English) 
Author:

Gregor, Jiří 
Language:

English 
Journal:

Aplikace matematiky 
ISSN:

03736725 
Volume:

26 
Issue:

2 
Year:

1981 
Pages:

142153 
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 
. 
Date available:

20080520T18:16:37Z 
Last updated:

20150709 
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. 824840. 
Reference:

[2] M. Fiedler: .Private communication, 1979. Zbl 0431.15005 
Reference:

[3] J. Gregor: Multivariable positive real functions.Res. Rep. III31/3, 1978 (in Czech). 
Reference:

[4] T. Kоgа: Synthesis of finite passive Nports with prescribed positive real matrices of several variables.IEEE Trans, on Circuit Th., Vol. CT15, No. 1, March 1968, pp. 223. 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. 
. 