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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

1992 • Question 7

Question

Math 6210 • Real Analysis 1992 • Question 7

Show that every continuous function on \(\overline {\Delta }=\{z:|z|\le 1\}\) which is holomorphic on \(\Delta =\{z:|z|<1\}\) can be uniformly approximated on \(\overline {\Delta }\) by holomorphic polynomials.

Raw LaTeX

Show that every continuous function on
\(\overline{\Delta}=\{z:|z|\le 1\}\) which is holomorphic on
\(\Delta=\{z:|z|<1\}\) can be uniformly approximated on \(\overline{\Delta}\) by
holomorphic polynomials.

Topic Tags

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