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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Summer 2018 • Question 10

Question

Math 6210 • Real Analysis Summer 2018 • Question 10

If \(f,g\) are entire functions and \(|f(z)|\le |g(z)|\) for all \(z\), then there exists \(c\in \mathbb C\) so that \[ f(z)=c\,g(z). \]

Raw LaTeX

If \(f,g\) are entire functions and \(|f(z)|\le |g(z)|\) for all
\(z\), then there exists \(c\in\mathbb C\) so that
\[
f(z)=c\,g(z).
\]

Topic Tags

Entire Functions and Liouville-Type Theorems