English
1987
ISBN: 081763147X
PDF
pages: 210

Written by an international specialist on complex approximation, this book is an authoritative and up-to-date introduction to the field. Gaier begins his presentation with a study of the classical constructive methods and then leads to more theoretical developments.

The first part deals with the classical theory of approximation in the complex domain, characterized by L2 expansions, the Bergman kernel function, Faber polynomials, and interpolation. The second part contains more modern results such as the theorems of Mergelyan, Alice Roth, Arakeljan, and Nersesjan，as well as applications to the construction of holomorphic functions with complicated boundary behavior.

This useful and practical book will be an appropriate introduction to the field for graduate students and instructors in mathematics.

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