Vitushkin's Conjecture for Removable Sets (Paperback, Edition.)

Vitushkin's conjecture, a special case of Painlev 's problem, states that a compact subset of the complex plane with finite linear Hausdorff measure is removable for bounded analytic functions if and only if it intersects every rectifiable curve in a set of zero arclength measure. Chapters 1-5 of the book provide important background material on removability, analytic capacity, Hausdorff measure, arclength measure, and Garabedian duality that will appeal to many analysts with interests independent of Vitushkin's conjecture. The fourth chapter contains a proof of Denjoy's conjecture that employs Melnikov curvature. A brief postscript reports on a deep theorem of Tolsa and its relevance to going beyond Vitushkin's conjecture. This text can be used for a topics course or seminar in complex analysis. To understand it, the reader should have a firm grasp of basic real and complex analysis.

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Universitext
Release date:	September 2010
First published:	2010
Authors:	James Dudziak
Dimensions:	235 x 155 x 19mm (L x W x T)
Format:	Paperback
Pages:	332
Edition:	Edition.
ISBN-13:	978-1-4419-6708-4
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis Promotions
LSN:	1-4419-6708-7
Barcode:	9781441967084

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