Complex Analysis

The book constitutes a basic, concise, yet rigorous course in complex analysis, for students who have studied calculus in one and several variables, but have not previously been exposed to complex ana

This text covers many principal topics in the theory of functions of a complex variable. These include, in real analysis, set algebra, measure and topology, real- and complex-valued functions, and top

Classical Complex Analysis, available in two volumes, provides a clear, broad and solid introduction to one of the remarkable branches of exact science, with an emphasis on the geometric aspects of an

Classical Complex Analysis, available in two volumes, provides a clear, broad and solid introduction to one of the remarkable branches of exact science, with an emphasis on the geometric aspects of an

A clear, self-contained treatment of important areas in complex analysis, this text is geared toward upper-level undergraduates and graduate students. Chiefly classical in content, it emphasizes the g

All the exercises plus their solutions for Serge Lang's fourth edition of "Complex Analysis," ISBN 0-387-98592-1. The problems in the first 8 chapters are suitable for an introductory course at underg

With its emphasis on the argument principle in analysis and topology, this book represents a different approach to the teaching of complex analysis. The three-part treatment provides geometrical insig

Romanian Finnish Seminar on Complex Analysis

This book shows how operator theory interacts with function theory in one and several variables. The authors develop the theory in detail, leading the reader to the cutting edge of contemporary research. It starts with a treatment of the theory of bounded holomorphic functions on the unit disc. Model theory and the network realization formula are used to solve Nevanlinna-Pick interpolation problems, and the same techniques are shown to work on the bidisc, the symmetrized bidisc, and other domains. The techniques are powerful enough to prove the Julia-Carathéodory theorem on the bidisc, Lempert's theorem on invariant metrics in convex domains, the Oka extension theorem, and to generalize Loewner's matrix monotonicity results to several variables. In Part II, the book gives an introduction to non-commutative function theory, and shows how model theory and the network realization formula can be used to understand functions of non-commuting matrices.

The central theme of this reference book is the metric geometry of complex analysis in several variables. Bridging a gap in the current literature, the text focuses on the fine behavior of the Kobayas

Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: complex a

This volume highlights the main results of the research performed within the network “Harmonic and Complex Analysis and its Applications” (HCAA), which was a five-year (2007–2012) European Science Fou

Mathematicians Jarnicki (Jagiellonian U., Krakow, Poland) and Pflug (Carl von Ossietzky U. Oldenburg, Germany) present a systematic study of invariant pseudo-distances and their infinitesimal counterp

This book is an outgrowth of the special summer session held at the Max Planck Institute for Mathematics and the Hausdorff Research Institute for Mathematics. The contributions in the volume provide a

This book gives a comprehensive introduction to complex analysis in several variables. It clearly focusses on special topics in complex analysis rather than trying to encompass as much material as pos

Presented from the point of view of modern work in the field, this book addresses advanced topics in complex analysis that verge on current areas of research. It adroitly weaves through a variety of t

Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solut

Over 1500 problems on theory of functions of the complex variable; coverage of nearly every branch of classical function theory. Topics include conformal mappings, integrals and power series, Laurent

This proceedings volume provides unique insights into the power of abstract methods and techniques in dealing successfully with a number of applications stemming from classical analysis and mathematic

The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in the first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. Volume 1 focuses on the analysis of real-valued functions of a real variable. Volume 2 goes on to consider metric and topological spaces. This third volume develops the classical theory of functions of a complex variable. It carefully establishes the properties of the complex plane, including a proof of the Jordan curve theorem. Lebesgue measure is introduced, and is used as a model for other measure spaces, where the theory of integration is developed. The Radon–Nikodym theorem is proved, and the differentiation of measures discussed.

This book discusses a variety of topics in mathematics and engineering as well as their applications, clearly explaining the mathematical concepts in the simplest possible way and illustrating them wi

This book covers the historical development of conformal inequalities and the universal interest in the Bieberback conjecture and its impact on creative thinking in mathematics over the last century.

The book contains 13 articles, some of which are survey articles and others research papers. Written by eminent mathematicians, these articles were presented at the International Workshop on Complex A