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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6220 • Complex Analysis

Summer 2022 • Question 2

Question

Math 6220 • Complex Analysis Summer 2022 • Question 2

Show that if \(f\) is holomorphic on \(\mathbb {D}\setminus \{0\}\) and

\[ \lim _{z\to 0} zf(z)=0 \]

then \(f\) can be extended to a holomorphic function on \(\mathbb {D}\).

Raw LaTeX

Show that if \(f\) is holomorphic on \(\mathbb{D}\setminus\{0\}\) and

\[
\lim_{z\to0} zf(z)=0
\]


then \(f\) can be extended to a holomorphic function on \(\mathbb{D}\).

Topic Tags

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