000 03214nam a22005415i 4500
001 978-3-540-36074-2
003 DE-He213
005 20190213151130.0
007 cr nn 008mamaa
008 100806s2002 gw | s |||| 0|eng d
020 _a9783540360742
_9978-3-540-36074-2
024 7 _a10.1007/b84244
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBK
_2thema
082 0 4 _a515
_223
100 1 _aPajot, Hervé.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aAnalytic Capacity, Rectifiability, Menger Curvature and the Cauchy Integral
_h[electronic resource] /
_cby Hervé Pajot.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2002.
300 _aVIII, 119 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1799
505 0 _aPreface -- Notations and conventions -- Some geometric measures theory -- Jones' traveling salesman theorem -- Menger curvature -- The Cauchy singular integral operator on Ahlfors-regular sets -- Analytic capacity and the Painlevé Problem -- The Denjoy and Vitushkin conjectures -- The capacity $gamma (+)$ and the Painlevé Problem -- Bibliography -- Index.
520 _aBased on a graduate course given by the author at Yale University this book deals with complex analysis (analytic capacity), geometric measure theory (rectifiable and uniformly rectifiable sets) and harmonic analysis (boundedness of singular integral operators on Ahlfors-regular sets). In particular, these notes contain a description of Peter Jones' geometric traveling salesman theorem, the proof of the equivalence between uniform rectifiability and boundedness of the Cauchy operator on Ahlfors-regular sets, the complete proofs of the Denjoy conjecture and the Vitushkin conjecture (for the latter, only the Ahlfors-regular case) and a discussion of X. Tolsa's solution of the Painlevé problem.
650 0 _aGlobal analysis (Mathematics).
650 0 _aGeometry.
650 0 _aMathematics.
650 0 _aFunctions of complex variables.
650 0 _aFourier analysis.
650 1 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
650 2 4 _aGeometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21006
650 2 4 _aMeasure and Integration.
_0http://scigraph.springernature.com/things/product-market-codes/M12120
650 2 4 _aFunctions of a Complex Variable.
_0http://scigraph.springernature.com/things/product-market-codes/M12074
650 2 4 _aFourier Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12058
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540000013
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1799
856 4 0 _uhttps://doi.org/10.1007/b84244
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c9628
_d9628