My Math Forum  

Go Back   My Math Forum > College Math Forum > Complex Analysis

Complex Analysis Complex Analysis Math Forum


Reply
 
LinkBack Thread Tools Display Modes
January 8th, 2011, 03:25 AM   #1
Newbie
 
Joined: Jan 2011

Posts: 2
Thanks: 0

Existance of analytic function at C - {0}

Problem:
Is there any analytic function that is bounded and non constant at domain of C - {0}?
If the answer is positive, I need an example of the function.
If the answer is negative, I need a proof.
vitalik.t is offline  
 
January 9th, 2011, 10:08 AM   #2
Newbie
 
Joined: Dec 2010

Posts: 18
Thanks: 0

Re: Existance of analytic function at C - {0}

Assume f is a bounded analytic function on C-{0}. Due to a theorem of Riemann on removable singularities, you can extend f analytically onto C where it is still bounded, hence constant due to Liouvilles Theorem. So the answer to your question is "No"!
Thommy is offline  
Reply

  My Math Forum > College Math Forum > Complex Analysis

Tags
analytic, existance, function



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Show function is not analytic WWRtelescoping Complex Analysis 1 February 25th, 2014 07:53 PM
What is an analytic function aaron-math Complex Analysis 4 October 14th, 2013 04:44 PM
Proving the non-existance of a function Decave Real Analysis 2 March 19th, 2013 01:07 AM
Continuous function existance (using probability) butabi Advanced Statistics 2 October 23rd, 2011 04:58 AM
analytic function krackwacker Complex Analysis 2 November 6th, 2008 10:19 PM





Copyright © 2019 My Math Forum. All rights reserved.