A Complex Analysis Problem Book

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Springer Science & Business Media, Aug 20, 2011 - Mathematics - 526 pages
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This is a collection of exercises in the theory of analytic functions, with completed and detailed solutions. We wish to introduce the student to applications and aspects of the theory of analytic functions not always touched upon in a first course. Using appropriate exercises we wish to show to the students some aspects of what lies beyond a first course in complex variables. We also discuss topics of interest for electrical engineering students (for instance, the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). Examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space) are given. The book also includes a part where relevant facts from topology, functional analysis and Lebesgue integration are reviewed.

 

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A lot of problems, including very hard ones. Very useful for a detailed and deep study of the subject from the basic definitions. Many problems can be found in other sources, but they are concentrated in one book, which is very comfortable.

Contents

Prologue
1
Part I Complex Numbers
9
Part II Functions of a Complex Variable
141
Part III Applications and More Advanced Topics
393
Part IV Appendix
447
Bibliography
512
Index
523
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About the author (2011)

Prof. Daniel Alpay is a faculty member of the department of mathematics at Ben-Gurion University, Beer-Sheva, Israel. He is the incumbent of the Earl Katz Family chair in algebraic system theory. He has a double formation of electrical engineer (Telecom Paris, graduated 1978) and mathematician (PhD, Weizmann Institute, 1986). His research includes operator theory, stochastic analysis, and the theory of linear systems. Daniel Alpay is one of the initiators and responsible of the dual track electrical-engineering mathematics at Ben-Gurion University. Together with co-authors, he has written two books and close to 190 research papers, and edited ten books of research papers.

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