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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 2007 • Question 6

Question

Math 6210 • Real Analysis Fall 2007 • Question 6

Let \(f\) be an entire function such that \(|f(z)|\le K|z|^n\) where \(K\) is a positive real constant and \(n\) is a positive integer. Show that \(f\) is a polynomial of degree \(\le n\).

Raw LaTeX

Let \(f\) be an entire function such that \(|f(z)|\le K|z|^n\) where
\(K\) is a positive real constant and \(n\) is a positive integer. Show that \(f\) is
a polynomial of degree \(\le n\).

Topic Tags

Entire Functions and Liouville-Type Theorems