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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 1994 • Question 9

Question

Math 6210 • Real Analysis Fall 1994 • Question 9

Suppose that \(f\) and \(g\) are one to one analytic functions of the open unit disk \(U=\{z\in \mathbb C:|z|<1\}\) onto some domain \(\Omega \). Suppose that \(f(0)=g(0)\), and \(f'(0)=g'(0)\ne 0\). Show that \(f(z)=g(z)\).

Raw LaTeX

Suppose that \(f\) and \(g\) are one to one analytic functions of the
open unit disk \(U=\{z\in\mathbb C:|z|<1\}\) onto some domain \(\Omega\). Suppose
that \(f(0)=g(0)\), and \(f'(0)=g'(0)\ne 0\). Show that \(f(z)=g(z)\).

Topic Tags

Analytic Continuation and Monodromy Holomorphic Functions and Cauchy-Riemann Equations