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100   $a20100806d2002      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aAnalytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral$b[electronic resource] /$fby Hervé M. Pajot
205   $a1st ed. 2002.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2002.
215   $a1 online resource (VIII, 119 p.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1799
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-540-00001-1 
320   $aIncludes bibliographical references (pages 115-118) and index.
327   $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.
330   $aBased on a graduate course given by the author at Yale University this book deals with complex analysis (analytic capacity), geometric measure theory (rectifiable and uniformly rectifiable sets) and harmonic analysis (boundedness of singular integral operators on Ahlfors-regular sets). In particular, these notes contain a description of Peter Jones' geometric traveling salesman theorem, the proof of the equivalence between uniform rectifiability and boundedness of the Cauchy operator on Ahlfors-regular sets, the complete proofs of the Denjoy conjecture and the Vitushkin conjecture (for the latter, only the Ahlfors-regular case) and a discussion of X. Tolsa's solution of the Painlevé problem.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1799
606   $aMathematical analysis
606   $aAnalysis (Mathematics)
606   $aGeometry
606   $aMeasure theory
606   $aFunctions of complex variables
606   $aFourier analysis
606   $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007
606   $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006
606   $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120
606   $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074
606   $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058
615  0$aMathematical analysis.
615  0$aAnalysis (Mathematics).
615  0$aGeometry.
615  0$aMeasure theory.
615  0$aFunctions of complex variables.
615  0$aFourier analysis.
615 14$aAnalysis.
615 24$aGeometry.
615 24$aMeasure and Integration.
615 24$aFunctions of a Complex Variable.
615 24$aFourier Analysis.
676   $a515/.42
700   $aPajot$b Hervé M$4aut$4http://id.loc.gov/vocabulary/relators/aut$01060269
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996466590203316
996   $aAnalytic Capacity, Rectifiability, Menger Curvature and Cauchy Integral$92512070
997   $aUNISA