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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Spring 2020 • Question 7

Question

Math 6210 • Real Analysis Spring 2020 • Question 7

Give an example of a sequence of numbers \(a_1,\ldots \) so that there is no holomorphic function \(f:\mathbb D\to \mathbb C\) so that \(a_1=f'(0)\), \(a_2=f''(0)\), \(a_3=f'''(0)\), \(\ldots \). Justify your answer.

Raw LaTeX

Give an example of a sequence of numbers \(a_1,\ldots\) so that
there is no holomorphic function \(f:\mathbb D\to\mathbb C\) so that
\(a_1=f'(0)\), \(a_2=f''(0)\), \(a_3=f'''(0)\), \(\ldots\). Justify your answer.

Topic Tags

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