Hermann Weyl considered value distribution theory to be the
greatest mathematical achievement of the first half of the 20th
century. The present lectures show that this beautiful theory is
still growing. An important tool is complex approximation and some
of the lectures are devoted to this topic. Harmonic approximation
started to flourish astonishingly rapidly towards the end of the
20th century, and the latest development, including approximation
manifolds, are presented here.
Since de Branges confirmed the Bieberbach conjecture, the
primary problem in geometric function theory is to find the precise
value of the Bloch constant. After more than half a century without
progress, a breakthrough was recently achieved and is presented.
Other topics are also presented, including Jensen measures.
A valuable introduction to currently active areas of complex
analysis and potential theory. Can be read with profit by both
students of analysis and research mathematicians.
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