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The Cauchy transform

Author: Joseph A Cima; Alec L Matheson; William T Ross
Publisher: Providence, R.I. : American Mathematical Society, [2006] ©2006
Series: Mathematical surveys and monographs, no. 125.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Cima, Joseph A., 1933-
Cauchy transform.
Providence, R.I. : American Mathematical Society, ©2006
(DLC) 2005055587
(OCoLC)62342207
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Joseph A Cima; Alec L Matheson; William T Ross
ISBN: 9781470413521 1470413523
OCLC Number: 879576567
Description: 1 online resource (ix, 272 pages) : illustrations.
Contents: 1. Preliminaries 2. The Cauchy transform as a function 3. The Cauchy transform as an operator 4. Topologies on the space of Cauchy transforms 5. Which functions are Cauchy integrals? 6. Multipliers and divisors 7. The distribution function for Cauchy transforms 8. The backward shift on $H^2$ 9. Clark measures 10. The normalized Cauchy transform 11. Other operators on the Cauchy transforms.
Series Title: Mathematical surveys and monographs, no. 125.
Responsibility: Joseph A. Cima, Alec L. Matheson, William T. Ross.
More information:

Abstract:

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.

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