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axterix
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 Cplx Problem   « on: Jul 22nd, 2005, 4:15pm » Quote Modify Remove

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 » Quote Modify

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 » Quote Modify Remove

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 » Quote Modify Remove

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 » Quote Modify

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 » Quote Modify

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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