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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.
American Mathematical Society
Providence, Rhode Island
perturbation theory, Clark measures, Cauchy transforms
School of Arts and Sciences
Math and Computer Science
Cima, Joseph A., Alec L. Matheson, and William T. Ross. The Cauchy Transform. Vol. 125. Providence, RI: American Mathematical Society, 2006.