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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

1999 • Question 6

Question

Math 6210 • Real Analysis 1999 • Question 6

Let \(U\) be the open unit disc in \(\mathbb C\). Let \(U^+\) be the intersection of \(U\) with the upper half plane.

(a) Let \(f(z)=\frac {1}{2}\left (z+\frac {1}{z}\right )\). Describe \(f(U^+)\).

(b) Give a conformal equivalence of \(U^+\) and \(U\).

Raw LaTeX

Let \(U\) be the open unit disc in \(\mathbb C\). Let \(U^+\) be the
intersection of \(U\) with the upper half plane.

(a) Let \(f(z)=\frac{1}{2}\left(z+\frac{1}{z}\right)\). Describe \(f(U^+)\).

(b) Give a conformal equivalence of \(U^+\) and \(U\).

Topic Tags

Argument Principle and Rouche's Theorem Conformal Moduli and Annuli