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Topic: existence of holomorphic log in simply-connected region not
containing {0}

Replies: 4   Last Post: Oct 13, 2012 12:20 PM

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Bacle H

Posts: 283
Registered: 4/8/12
existence of holomorphic log in simply-connected region not
containing {0}

Posted: Oct 11, 2012 7:37 PM
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Hi, All:

I'm looking for a proof of the existence of a holomorphic log in

a region R that are simply-connected but do not wind around the origin.

My idea is:

logz is defined as the integral Int_Gamma dz/z , for Gamma a simple-closed

curve. The log is then well-defined , since, in simply-connected regions,

the integral is independent of path. In addition, 1/z is holomorphic

since z=/0 in R . Then the integral is well-defined and holomorphic,

(integral of holomorphic function is holomorphic ) , so the log exists.

Is this O.K?


that



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