Application of Rouche’s theorem for MP filter design

2009 ◽  
Vol 211 (2) ◽  
pp. 329-335 ◽  
Author(s):  
Gordana Jovanovic Dolecek ◽  
Vlatko Dolecek
Keyword(s):  
Filter Design ◽  
Rouche’S Theorem ◽  
Rouché's Theorem

A Remark on Rouché's Theorem

1976 ◽  
Vol 83 (3) ◽  
pp. 186-187 ◽  
Author(s):  
I. Glicksberg
Keyword(s):  
Rouche’S Theorem ◽  
Rouché's Theorem

scholarly journals A local mean value theorem for the complex plane

1969 ◽  
Vol 16 (4) ◽  
pp. 329-331 ◽  
Author(s):  
J. M. Robertson
Keyword(s):  
Complex Plane ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Local Mean ◽  
Rouche’S Theorem ◽  
Image Position ◽  
Rouché's Theorem

The equationneed not have a solution z in the complex plane, even when ƒ is entire. For example, let ƒ(z) = ez, z1 = z0+2kπi. Thus the classical mean value theorem does not extend to the complex plane. McLeod has shown (2) that if ƒ is analytic on the segment joining z1 and z0, then there are points w1 and w2 on the segment such that where The purpose of this article is to give a local mean value theorem in the complex plane. We show that there is at least one point z satisfying (1), which we will call a mean value point, near z1 and z0 but not necessarily on the segment joining them, provided z1 and z0 are sufficiently close. The proof uses Rouché's Theorem (1).

scholarly journals Logarithmic residues, Rouché’s theorem, and spectral regularity: The C∗-algebra case

2012 ◽  
Vol 23 (4) ◽  
pp. 816-847 ◽  
Author(s):  
H. Bart ◽  
T. Ehrhardt ◽  
B. Silbermann
Keyword(s):  
Rouche’S Theorem ◽  
Rouché's Theorem
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