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 indepth treatment of Clark measures.
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Für höhere Schule und Studium
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ISBN-13
978-0-8218-3871-6 (9780821838716)
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Schweitzer Klassifikation
Overview Preliminaries The Cauchy transform as a function The Cauchy transform as an operator Topologies on the space of Cauchy transforms Which functions are Cauchy integrals? Multipliers and divisors The distribution function for Cauchy transforms The backward shift on $H^2$ Clark measures The normalized Cauchy transform Other operators on the Cauchy transforms List of symbols Bibliography Index.
