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Titlebook: Vitushkin’s Conjecture for Removable Sets; James J. Dudziak Book 2010 Springer Science+Business Media, LLC 2010 Analytic capacity.Arclengt

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发表于 2025-3-21 16:08:15 | 显示全部楼层 |阅读模式
书目名称Vitushkin’s Conjecture for Removable Sets
编辑James J. Dudziak
视频videohttp://file.papertrans.cn/984/983980/983980.mp4
概述Presents a complete proof of a major recent accomplishment of modern complex analysis, the affirmative resolution of Vitushkin‘s conjecture.Includes Melnikov and Verdera‘s proof of Denjoy‘s conjecture
丛书名称Universitext
图书封面Titlebook: Vitushkin’s Conjecture for Removable Sets;  James J. Dudziak Book 2010 Springer Science+Business Media, LLC 2010 Analytic capacity.Arclengt
描述.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 arc length measure.  Chapters 6-8 of this carefully written text present a major recent accomplishment of modern complex analysis, the affirmative resolution of this conjecture.  Four of the five mathematicians whose work solved Vitushkin‘s conjecture have won the prestigious Salem Prize in analysis.. Chapters 1-5 of this book provide important background material on removability, analytic capacity, Hausdorff measure, arc length 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.  Although standard notation is used throughout, there is a symbol glossary at the back of the book for the reader‘s convenience.. This text can be used for a topics course or se
出版日期Book 2010
关键词Analytic capacity; Arclength measure; Argument principle; Complex analysis; Garabedian duality; Hausdorff
版次1
doihttps://doi.org/10.1007/978-1-4419-6709-1
isbn_softcover978-1-4419-6708-4
isbn_ebook978-1-4419-6709-1Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer Science+Business Media, LLC 2010
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发表于 2025-3-21 21:15:03 | 显示全部楼层
0172-5939 Includes Melnikov and Verdera‘s proof of Denjoy‘s conjecture.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
发表于 2025-3-22 03:03:37 | 显示全部楼层
James J. Dudziak Besserung durchmacht, unabhängig davon, welche Behandlungsmaßnahmen ergriffen werden. Trotzdem gibt es einige Arbeiten, in denen es gelang, zwischen Erst- und Zweitge- neration-Antidepressiva zu differenzieren.
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发表于 2025-3-22 11:36:27 | 显示全部楼层
James J. Dudziak the gut lumen to the serum of the newborn occurs. The present preliminary studies are concerned with examining the kinetics of binding of rat and bovine IgG to isolated brushborders prepared from neonatal rat jejunum.
发表于 2025-3-22 13:47:32 | 显示全部楼层
James J. Dudziakfor altered sensitivity to drugs. Apart from the various factors known to influence pharmacokinetics of drugs in the elderly, as discussed in Chapter 8, other physical or mental illnesses and some social factors probably also contribute to this increased incidence of adverse effects.
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发表于 2025-3-22 21:28:14 | 显示全部楼层
Removable Sets and Hausdorff Measure, 2.1 through 2.4 below are enough to get us through to the end of Chapter 4. It is only after, in Section 5.1, that we shall need to take up the fact that Hausdorff measure is indeed a positive measure defined on a .-algebra containing the Borel subsets of ℂ!
发表于 2025-3-23 04:10:18 | 显示全部楼层
,A Solution to Vitushkin’s Conjecture Modulo Two Difficult Results,he converse becomes true when the compact set in question is restricted in some suitable way – in that case, restricted to be a subset of a rectifiable curve. The restriction to make in the case now facing us is clear because the Joyce–Mö;rters set, although of Hausdorff dimension one, has . linear Hausdorff measure (Proposition 4.34).
发表于 2025-3-23 07:57:18 | 显示全部楼层
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