# On quadratic Hurwitz forms. I

Aplikace matematiky (1981)

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

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topGregor, 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

top- N. K. Bose, Problems and Progress in Multidimensional Systems Theory, Proc. IEEE, Vol. 65, No. 6, June 1977, pp. 824-840. (1977)
- M. Fiedler, [unknown], Private communication, 1979. (1979) Zbl0431.15005
- J. Gregor, Multivariable positive real functions, Res. Rep. III-3-1/3, 1978 (in Czech). (1978)
- 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
- 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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