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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 1993 • Question 10

Question

Math 6210 • Real Analysis Fall 1993 • Question 10

Suppose \(f\) is an entire function and there exist \(M>0\), \(R>0\) and a number \(0<k<1\) such that \(|f(z)|\le M|z|^k\) for \(|z|\ge R\). Show \(f\) is a constant.

Raw LaTeX

Suppose \(f\) is an entire function and there exist \(M>0\), \(R>0\) and
a number \(0<k<1\) such that \(|f(z)|\le M|z|^k\) for \(|z|\ge R\). Show \(f\) is a
constant.

Topic Tags

Entire Functions and Liouville-Type Theorems