The Symmetric Versions of Rouché’s Theorem via ∂--Calculus
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-02-04
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
Let (f,g) be a pair of holomorphic functions.
In this expositional paper we apply the ∂--calculus to prove the symmetric version “|f+g|<|f|+|g| on ∂K” as well as the homotopic version of Rouché's theorem for arbitrary planar compacta K.
Using Eilenberg's representation theorem we also give a converse to the homotopic version.
Then we derive two analogs of Rouché's theorem for continuous-holomorphic pairs (a symmetric and a nonsymmetric one).
One of the rarely presented properties of the non-symmetric version is that in the fundamental boundary hypothesis, |f+g|≤|g|, equality is allowed.
American Psychological Association (APA)
Mortini, Raymond& Rupp, Rudolf. 2014. The Symmetric Versions of Rouché’s Theorem via ∂--Calculus. Journal of Complex Analysis،Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-458313
Modern Language Association (MLA)
Mortini, Raymond& Rupp, Rudolf. The Symmetric Versions of Rouché’s Theorem via ∂--Calculus. Journal of Complex Analysis No. 2014 (2014), pp.1-9.
https://search.emarefa.net/detail/BIM-458313
American Medical Association (AMA)
Mortini, Raymond& Rupp, Rudolf. The Symmetric Versions of Rouché’s Theorem via ∂--Calculus. Journal of Complex Analysis. 2014. Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-458313
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-458313