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The Cauchy Transform

About this Title

Joseph A. Cima, University of North Carolina, Chapel Hill, Chapel Hill, NC, Alec L. Matheson, Lamar University, Beaumont, TX and William T. Ross, University of Richmond, Richmond, VA

Publication: Mathematical Surveys and Monographs
Publication Year: 2006; Volume 125
ISBNs: 978-0-8218-3871-6 (print); 978-1-4704-1352-1 (online)
DOI: https://doi.org/10.1090/surv/125
MathSciNet review: MR2215991
MSC: Primary 30-02; Secondary 30E10, 30E20, 46E15, 46E20, 46E22, 47B33, 47B38

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Table of Contents

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Front/Back Matter

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Chapters

• 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