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   Author  Topic: Cplx Problem  (Read 2477 times)
axterix
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Cplx Problem  
« on: Jul 22nd, 2005, 4:15pm »
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Find all function f analytic in the disk D such that |z| < R which satisfies f(0) = i and |f(z)| <=1 or all z in D, and where R is any number greater than zero.
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Michael Dagg
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Re: Cplx Problem  
« Reply #1 on: Jul 23rd, 2005, 9:01am »
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This problem slightly misstated. There is only one such function and it is f(z) = i.
 
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Michael Dagg
axterix
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Re: Cplx Problem  
« Reply #2 on: Jul 26th, 2005, 9:21pm »
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That is the right answer but what part is wrong?
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axterix
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Re: Cplx Problem  
« Reply #3 on: Jul 26th, 2005, 9:36pm »
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Ah, never mind - I see it.
 
How do you know or how did show that there is only one function f(z) = i that satisfies the properties?
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Eigenray
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Re: Cplx Problem  
« Reply #4 on: Jul 27th, 2005, 10:56am »
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Read up on the maximum modulus principle.  Or the open mapping theorem.
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Michael Dagg
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Re: Cplx Problem  
« Reply #5 on: Jul 27th, 2005, 12:04pm »
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The problem is a frequent exercise in CA books and is generally associated with the first hint Eigenray gave.
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Michael Dagg
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