The Cauchy transform of a measure on the circle is a subject of both classical and current interest with a sizable literature. This book is a thorough, well-documented, and readable survey of this literature and includes full proofs of the main results of the subject. This book also covers more recent perturbation theory as covered by Clark, Poltoratski, and Aleksandrov and contains an in-depth treatment of Clark measures. Readership Graduate students and research mathematicians interested in classical and modern complex analysis. Reviews "Proofs are presented very carefully, so that the whole material becomes accessible to any graduate student interested in analysis. Experienced researchers will also be thankful to the authors for having presented them this material for the first time. We recommend this survey to any person interested in function theory and operator theory on the disk." *-- Zentralblatt MATH* "The book is user-friendly it is clearly written, at an agreeable pace. Many of the deepest results of the theory are afforded complete treatments. Scattered throughout are mentions of related results, with references to the literature. The authors are thorough and meticulous in their citation of references." *-- Mathematical Reviews* "...contains a wealth of interesting results, presented in an attractive and readable style..." *-- Bulletin of the LMS* "Combining both classical and recent result, the book presents a great interest for students, teachers and researchers interested mainly in functional analysis methods in complex analysis. The topics are presented in an elegant manner, with many comments, detours and historical references. The result is a fine book that deserves to be on the bookshelf of each analyst." *-- Studia Universitatis Babes-Bolyai, Mathematica* |