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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
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Category: math
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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
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Date available: 2008-05-20T18:16:37Z
Last updated: 2015-07-09
Stable URL: http://hdl.handle.net/10338.dmlcz/103904
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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.
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