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Bulletin of the London Mathematical Society Advance Access originally published online on January 16, 2007
Bulletin of the London Mathematical Society 2007 39(1):169-172; doi:10.1112/blms/bdl021
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© 2006 London Mathematical Society

Book Review

The Cauchy Transform

(Mathematical Surveys and Monographs 125)

By Joseph A. Cima, Alec L. Matheson and William T. Ross:

272 pp., £43.75 (US$75), ISBN 0-8218-3871-7

(American Mathematical Society, Providence, RI, 2006).

The first 10% of the full text of this article appears below.

In the border country between complex analysis, harmonic analysis and differential equations, there can be found many popular transforms, of which those of Fourier and Laplace are probably the most commonly used. This book is concerned with another one, which is more rarely sighted.

The Cauchy transform of a finite complex measure µ defined on the unit circle T in the complex plane is the analytic function Kµ defined by


Formula 021UM1

for z in the unit disc D. Its name derives from the observation that Cauchy's integral formula, when applied to an analytic function f, is equivalent to the statement that the Cauchy transform of the measure Formula is just . . . [Full Text of this Article]

Jonathan R. Partington

University of Leeds


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