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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

2003 • Question 8

Question

Math 6210 • Real Analysis 2003 • Question 8

Suppose \(f\) is continuous on \(U=\{z\in \mathbb C: |z|<1\}\) and holomorphic on the complement in \(U\) of the interval \((-1,1)\). Prove that \(f\) is actually holomorphic on \(U\).

Raw LaTeX

Suppose \(f\) is continuous on \(U=\{z\in\mathbb C: |z|<1\}\) and
holomorphic on the complement in \(U\) of the interval \((-1,1)\). Prove that \(f\) is
actually holomorphic on \(U\).

Topic Tags

Holomorphic Functions and Cauchy-Riemann Equations Holomorphic Roots and Logarithms Zeros of Holomorphic Functions and the Identity Theorem