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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

2006 • Question 8

Question

Math 6210 • Real Analysis 2006 • Question 8

Suppose \(f\) is an entire function with \(f^{(n)}(0)\ge 0\) for all non-negative integers \(n\). Find a point at which \(|f(z)|\) assumes its maximum on \(\overline {D_R}(0)\) and tell what that maximum is. Justify your answer.

Raw LaTeX

Suppose \(f\) is an entire function with \(f^{(n)}(0)\ge 0\) for all
non-negative integers \(n\). Find a point at which \(|f(z)|\) assumes its maximum on
\(\overline{D_R}(0)\) and tell what that maximum is. Justify your answer.

Topic Tags

Entire Functions and Liouville-Type Theorems