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

top
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

top

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

top
  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) Zbl0495.32001MR0601594
  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) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.