On quadratic Hurwitz forms. I

Jiří Gregor

Aplikace matematiky (1981)

  • Volume: 26, Issue: 2, page 142-153
  • ISSN: 0862-7940

Abstract

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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 Γ ( n ) = z ∈ C ( n ) : R e z > 0 . Conclusions for the theory of multivariable positive real functions are formulated with applications in multivariable electrical network theory.

How to cite

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Gregor, Jiří. "On quadratic Hurwitz forms. I." Aplikace matematiky 26.2 (1981): 142-153. <http://eudml.org/doc/15189>.

@article{Gregor1981,
abstract = {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\lbrace z\in C^\{(n)\}:\text\{R\}e \ z>0\right\rbrace $. Conclusions for the theory of multivariable positive real functions are formulated with applications in multivariable electrical network theory.},
author = {Gregor, Jiří},
journal = {Aplikace matematiky},
keywords = {Hurwitz polynomial; electrical networks; Hurwitz polynomial; electrical networks},
language = {eng},
number = {2},
pages = {142-153},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On quadratic Hurwitz forms. I},
url = {http://eudml.org/doc/15189},
volume = {26},
year = {1981},
}

TY - JOUR
AU - Gregor, Jiří
TI - On quadratic Hurwitz forms. I
JO - Aplikace matematiky
PY - 1981
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 26
IS - 2
SP - 142
EP - 153
AB - 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\lbrace z\in C^{(n)}:\text{R}e \ z>0\right\rbrace $. Conclusions for the theory of multivariable positive real functions are formulated with applications in multivariable electrical network theory.
LA - eng
KW - Hurwitz polynomial; electrical networks; Hurwitz polynomial; electrical networks
UR - http://eudml.org/doc/15189
ER -

References

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  1. N. K. Bose, Problems and Progress in Multidimensional Systems Theory, Proc. IEEE, Vol. 65, No. 6, June 1977, pp. 824-840. (1977) 
  2. M. Fiedler, [unknown], Private communication, 1979. (1979) Zbl0431.15005
  3. J. Gregor, Multivariable positive real functions, Res. Rep. III-3-1/3, 1978 (in Czech). (1978) 
  4. T. Kоgа, 10.1109/TCT.1968.1082780, IEEE Trans, on Circuit Th., Vol. CT-15, No. 1, March 1968, pp. 2-23. (1968) DOI10.1109/TCT.1968.1082780
  5. M. A. Lavrentyev B. V. Shabat, Methods of the Theory of Functions of a Complex Variable, (in Russian). FIZMATGIZ, Moscow 1958. (1958) 

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