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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

1992 • Question 9

Question

Math 6210 • Real Analysis 1992 • Question 9

Suppose \(f\) is holomorphic in \(\{z:|z|<1\}\) and satisfies \(|f(\frac {1}{n})|\le (\frac {1}{n})^n\) for \(n=2,3,\ldots \). Can you identify \(f\)? Justify your answer.

Raw LaTeX

Suppose \(f\) is holomorphic in \(\{z:|z|<1\}\) and satisfies
\(|f(\frac{1}{n})|\le(\frac{1}{n})^n\) for \(n=2,3,\ldots\). Can you identify \(f\)?
Justify your answer.

Topic Tags

Holomorphic Functions and Cauchy-Riemann Equations Holomorphic Roots and Logarithms Zeros of Holomorphic Functions and the Identity Theorem