Determine, with motivation, all funtions that is analytic on

{z/ |z| < 4}, with f( 0 ) = i and |f( z ) <= 1 on {z/ |z| < 4}

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- March 19th 2008, 06:18 AMJacquesRouxComplex Analysis
Determine, with motivation, all funtions that is analytic on

{z/ |z| < 4}, with f( 0 ) = i and |f( z ) <= 1 on {z/ |z| < 4} - March 19th 2008, 04:00 PMThePerfectHacker
It seems your problem is faulty somehow. Because the way it is stated is the only such mapping. Because if is non-constant then by the open mapping theorem has to be a mapped into an interior point of the range of but that is not possible since is a boundary point. Thus, we conclude that constant functions are the only such functions, thus, for all .

- March 19th 2008, 11:50 PMJacquesRoux
Thanks for your help!