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A PROBABILISTIC PROOF OF THE OPEN MAPPING THEOREM FOR ANALYTIC FUNCTIONS

Part of: Markov processes General properties

Published online by Cambridge University Press:  17 December 2013

GREG MARKOWSKY
GREG MARKOWSKY*
Affiliation:
Monash University, Victoria 3800, Australia email gmarkowsky@gmail.com
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Abstract

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The conformal invariance of Brownian motion is used to give a short proof of the Open Mapping theorem for analytic functions.

Keywords

analytic functions; Open Mapping theorem; Brownian motion

MSC classification

Secondary: 30A99: None of the above, but in this section 60J65: Brownian motion
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 1 , August 2014 , pp. 74 - 76
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

Durrett, R., Brownian Motion and Martingales in Analysis (Wadsworth Advanced Books and Software, Belmont, CA, 1984).Google Scholar
Revuz, D. and Yor, M., Continuous Martingales and Brownian Motion (Springer, Berlin, 1999).Google Scholar
Rudin, W., Real and Complex Analysis (Tata McGraw-Hill, New York, 1987).Google Scholar