000			03079nam a22004215i 4500
001			u371730
003			SIRSI
005			20160812080144.0
007			cr nn 008mamaa
008			110201s2010 xxu| s |||| 0|eng d
020			_a9781441967091 _9978-1-4419-6709-1
040			_cMX-MeUAM
050		4	_aQA331.7
082	0	4	_a515.94 _223
100	1		_aDudziak, James J. _eauthor.
245	1	0	_aVitushkin’s Conjecture for Removable Sets _h[recurso electrónico] / _cby James J. Dudziak.
264		1	_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2010.
300			_aXII, 272p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUniversitext, _x0172-5939
505	0		_aRemovable Sets and Analytic Capacity -- Removable Sets and Hausdorff Measure -- Garabedian Duality for Hole-Punch Domains -- Melnikov and Verdera’s Solution to the Denjoy Conjecture -- Some Measure Theory -- A Solution to Vitushkin’s Conjecture Modulo Two Difficult Results -- The T(b) Theorem of Nazarov, Treil, and Volberg -- The Curvature Theorem of David and Léger.
520			_aVitushkin'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 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, 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. 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 seminar in complex analysis. To understand it, the reader should have a firm grasp of basic real and complex analysis.
650		0	_aMathematics.
650		0	_aDifferential equations, partial.
650	1	4	_aMathematics.
650	2	4	_aSeveral Complex Variables and Analytic Spaces.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781441967084
830		0	_aUniversitext, _x0172-5939
856	4	0	_zLibro electrónico _uhttp://148.231.10.114:2048/login?url=http://link.springer.com/book/10.1007/978-1-4419-6709-1
596			_a19
942			_cLIBRO_ELEC
999			_c199610 _d199610