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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 2010 • Question 9

Question

Math 6210 • Real Analysis Fall 2010 • Question 9

Let \(n\) be a positive integer. Denote by \(V_n\) the linear space of all entire functions \(f\) such that there exists \(C>0\) such that \(|f(z)|\le C|z|^n\) for all \(z\in \mathbb C\).

(i) Describe precisely the functions in \(V_n\);

(ii) Find the dimension of \(V_n\).

Raw LaTeX

Let \(n\) be a positive integer. Denote by \(V_n\) the linear space of
all entire functions \(f\) such that there exists \(C>0\) such that
\(|f(z)|\le C|z|^n\) for all \(z\in\mathbb C\).

(i) Describe precisely the functions in \(V_n\);

(ii) Find the dimension of \(V_n\).

Topic Tags

Entire Functions and Liouville-Type Theorems