A multiplication theorem for two-variable positive real matrices

Fazlollah M. Reza

Aplikace matematiky (1985)

  • Volume: 30, Issue: 4, page 291-296
  • ISSN: 0862-7940

Abstract

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A multiplication-division theorem is derived for the positive real functions of two complex variables. The theorem is generalized to encompass the product of positive real functions of two complex variables. The theorem is generalized to encompass the product of positive real matrices whose elements are functions of two complex variables. PRF and PR matrices occur frequantly in the study of electrical multiports and multivariable systems (such as digital filters).

How to cite

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Reza, Fazlollah M.. "A multiplication theorem for two-variable positive real matrices." Aplikace matematiky 30.4 (1985): 291-296. <http://eudml.org/doc/15407>.

@article{Reza1985,
abstract = {A multiplication-division theorem is derived for the positive real functions of two complex variables. The theorem is generalized to encompass the product of positive real functions of two complex variables. The theorem is generalized to encompass the product of positive real matrices whose elements are functions of two complex variables. PRF and PR matrices occur frequantly in the study of electrical multiports and multivariable systems (such as digital filters).},
author = {Reza, Fazlollah M.},
journal = {Aplikace matematiky},
keywords = {positive real functions},
language = {eng},
number = {4},
pages = {291-296},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A multiplication theorem for two-variable positive real matrices},
url = {http://eudml.org/doc/15407},
volume = {30},
year = {1985},
}

TY - JOUR
AU - Reza, Fazlollah M.
TI - A multiplication theorem for two-variable positive real matrices
JO - Aplikace matematiky
PY - 1985
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 30
IS - 4
SP - 291
EP - 296
AB - A multiplication-division theorem is derived for the positive real functions of two complex variables. The theorem is generalized to encompass the product of positive real functions of two complex variables. The theorem is generalized to encompass the product of positive real matrices whose elements are functions of two complex variables. PRF and PR matrices occur frequantly in the study of electrical multiports and multivariable systems (such as digital filters).
LA - eng
KW - positive real functions
UR - http://eudml.org/doc/15407
ER -

References

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  1. N. K. Bose, Applied Multidimensional Systems Theory, Van Nostrand Reinhold C., New York, 1982. (1982) Zbl0574.93031MR0652483
  2. W. Rudin, Function Theory in the Unit Ball of C n , Springer, Berlin, 1980. (1980) MR0601594
  3. S. G. Krantz, Function Theory of Several Complex Variables, John Wiley and Sons, New York, 1982. (1982) Zbl0471.32008MR0635928
  4. A. Fettweis G. Linnenberg, A Class of Two- Dimensional Reactance Functions With Applications, Archiv. Für Elektronik und Übertragungstechnik, vol. 34 (1980), pp. 276-278. (1980) 
  5. J. Gregor, On Quadratic Hurwitz Forms, Aplikace Matematiky 26 (1981), pp. 142-153. (1981) Zbl0457.15016MR0612670
  6. T. Kоgа, Synthesis of Finite Passive n-Ports with Prescribed Two-variable Reactance Matrices, JEEE vol. CT- 13 (1966), pp. 31 - 52. (1966) 
  7. F. M. Reza, Product of Inductive and Capacitive Operators, IEE Proc. vol. 129, Pt. G. No. 5, October 1982, pp. 241-244. (1982) 

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