A Complex Analysis Problem Book, 2nd Edition

Authors: Daniel Alpay



Features a new chapter on rational functions

Elaborates on connections with electrical engineering and the theory of linear systems

Uses a variety of non-trivial and interesting examples as the basis for exercises (e.g. the Bohr phenomenon, integral representations of certain analytic functions, Blaschke products, and the Schur algorithm)

Some of the exercises use the notions of positive matrix, positive definite function and reproducing kernel Hilbert space

This second edition presents a collection of exercises on the theory of analytic functions, including completed and detailed solutions. It introduces students to various applications and aspects of the theory of analytic functions not always touched on in a first course, while also addressing topics of interest to electrical engineering students (e.g., the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). It provides examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space), and also includes a section reviewing essential aspects of topology, functional analysis and Lebesgue integration.

Benefits of the 2nd edition
Rational functions are now covered in a separate chapter. Further, the section on conformal mappings has been expanded.