Vitushkin s Conjecture for Removable Sets is popular PDF and ePub book, written by James Dudziak in 2011-02-03, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Vitushkin s Conjecture for Removable Sets can be Read Online from any device for your convenience.
Vitushkin s Conjecture for Removable Sets Book PDF Summary
Vitushkin's conjecture, a special case of Painlevé'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.
Detail Book of Vitushkin s Conjecture for Removable Sets PDF
- Author : James Dudziak
- Release : 03 February 2011
- Publisher : Springer Science & Business Media
- ISBN : 9781441967091
- Genre : Mathematics
- Total Page : 338 pages
- Language : English
- PDF File Size : 15,7 Mb
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