MR1992
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### Questions (5)

 4 Doesn't a function with constant modulus on the boundary of a bounded domain have constant modulus over the entire domain? 3 Prove partial derivatives of uniformly convergent harmonic functions converge to the partial derivative of the limit of the sequence. 3 Prove that the orbit of an iterated rotation of 0 (by (A)(Pi), A irrational) around a circle centered at the origin is dense in the circle. 2 $S$ is a subgroup of index $f$. Show that $fxS=S$ where $fx$ is $x^{f}$ and $fxS$ the left coset. 1 Given two fixed points on unit disk,find analytic functions from unit disk to unit disk that maximize the distance between values at the two points

### Reputation (70)

 +5 Doesn't a function with constant modulus on the boundary of a bounded domain have constant modulus over the entire domain? +5 Prove partial derivatives of uniformly convergent harmonic functions converge to the partial derivative of the limit of the sequence. +5 Given two fixed points on unit disk,find analytic functions from unit disk to unit disk that maximize the distance between values at the two points +5 Prove that the orbit of an iterated rotation of 0 (by (A)(Pi), A irrational) around a circle centered at the origin is dense in the circle.

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### Tags (9)

 0 complex-analysis × 3 0 abstract-algebra 0 dynamical-systems 0 harmonic-analysis 0 general-topology 0 analysis 0 real-analysis 0 abelian-groups 0 group-theory

### Account (1)

 Mathematics 70 rep 4