My Math Forum Analytic

 Complex Analysis Complex Analysis Math Forum

 February 23rd, 2009, 01:38 PM #1 Newbie   Joined: Feb 2009 Posts: 7 Thanks: 0 Analytic show that if f(z) is analytic and real valued in a domain D then f(z) is constant in D.
 February 23rd, 2009, 05:19 PM #2 Member   Joined: Jan 2009 Posts: 72 Thanks: 0 Re: Analytic Harmonic conjugates are unique to within constants. The harmonic conjugate of the imagimary part of given function is a constant. Since the imag part is zero, the function is a constant. This uses a powerful result. A direct proof, say from the C-R equations, would be better.
 February 24th, 2009, 05:50 AM #3 Senior Member   Joined: Jan 2009 From: Russia Posts: 113 Thanks: 0 Re: Analytic Morera's theorem also helps here.
February 24th, 2009, 02:09 PM   #4
Global Moderator

Joined: May 2007

Posts: 6,850
Thanks: 742

Re: Analytic

Quote:
 Originally Posted by srw899 show that if f(z) is analytic and real valued in a domain D then f(z) is constant in D.
You need to put some restriction on D. For example if D is the real line and f(z) is a polynomial in z with real coefficients, the statement does not hold.

February 27th, 2009, 09:10 AM   #5
Member

Joined: Jan 2009

Posts: 72
Thanks: 0

Re: Analytic

Good point

Quote:
 Originally Posted by mathman You need to put some restriction on D. For example if D is the real line and f(z) is a polynomial in z with real coefficients, the statement does not hold.
Is not a domain defined to be open? connected? Are these enough, or must we also require boundedness, for example?

 Tags analytic

### is z conjugate analytic/mathforum

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post aaron-math Complex Analysis 4 October 14th, 2013 05:44 PM GgiPunjab Number Theory 1 January 8th, 2013 06:24 AM Geometry 1 December 15th, 2012 09:36 AM Ivahnesh Complex Analysis 1 December 17th, 2009 02:34 PM Samantha Algebra 2 August 24th, 2007 10:55 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top