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Analytic Capacity, Rectifiability, Menger Curvature and the Cauchy Integral [electronic resource] /
Based 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.
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| Format: | Texto biblioteca |
| Language: | eng |
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Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,
2002
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| Subjects: | Mathematics., Mathematical analysis., Analysis (Mathematics)., Fourier analysis., Functions of complex variables., Measure theory., Geometry., Analysis., Measure and Integration., Functions of a Complex Variable., Fourier Analysis., |
| Online Access: | http://dx.doi.org/10.1007/b84244 |
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KOHA-OAI-TEST:2236942018-07-31T00:03:04ZAnalytic Capacity, Rectifiability, Menger Curvature and the Cauchy Integral [electronic resource] / Pajot, Hervé. author. SpringerLink (Online service) textBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,2002.engBased 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.Preface -- 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.Based 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.Mathematics.Mathematical analysis.Analysis (Mathematics).Fourier analysis.Functions of complex variables.Measure theory.Geometry.Mathematics.Analysis.Geometry.Measure and Integration.Functions of a Complex Variable.Fourier Analysis.Springer eBookshttp://dx.doi.org/10.1007/b84244URN:ISBN:9783540360742 |
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COLPOS |
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México |
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biblioteca |
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America del Norte |
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Departamento de documentación y biblioteca de COLPOS |
| language |
eng |
| topic |
Mathematics. Mathematical analysis. Analysis (Mathematics). Fourier analysis. Functions of complex variables. Measure theory. Geometry. Mathematics. Analysis. Geometry. Measure and Integration. Functions of a Complex Variable. Fourier Analysis. Mathematics. Mathematical analysis. Analysis (Mathematics). Fourier analysis. Functions of complex variables. Measure theory. Geometry. Mathematics. Analysis. Geometry. Measure and Integration. Functions of a Complex Variable. Fourier Analysis. |
| spellingShingle |
Mathematics. Mathematical analysis. Analysis (Mathematics). Fourier analysis. Functions of complex variables. Measure theory. Geometry. Mathematics. Analysis. Geometry. Measure and Integration. Functions of a Complex Variable. Fourier Analysis. Mathematics. Mathematical analysis. Analysis (Mathematics). Fourier analysis. Functions of complex variables. Measure theory. Geometry. Mathematics. Analysis. Geometry. Measure and Integration. Functions of a Complex Variable. Fourier Analysis. Pajot, Hervé. author. SpringerLink (Online service) Analytic Capacity, Rectifiability, Menger Curvature and the Cauchy Integral [electronic resource] / |
| description |
Based 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. |
| format |
Texto |
| topic_facet |
Mathematics. Mathematical analysis. Analysis (Mathematics). Fourier analysis. Functions of complex variables. Measure theory. Geometry. Mathematics. Analysis. Geometry. Measure and Integration. Functions of a Complex Variable. Fourier Analysis. |
| author |
Pajot, Hervé. author. SpringerLink (Online service) |
| author_facet |
Pajot, Hervé. author. SpringerLink (Online service) |
| author_sort |
Pajot, Hervé. author. |
| title |
Analytic Capacity, Rectifiability, Menger Curvature and the Cauchy Integral [electronic resource] / |
| title_short |
Analytic Capacity, Rectifiability, Menger Curvature and the Cauchy Integral [electronic resource] / |
| title_full |
Analytic Capacity, Rectifiability, Menger Curvature and the Cauchy Integral [electronic resource] / |
| title_fullStr |
Analytic Capacity, Rectifiability, Menger Curvature and the Cauchy Integral [electronic resource] / |
| title_full_unstemmed |
Analytic Capacity, Rectifiability, Menger Curvature and the Cauchy Integral [electronic resource] / |
| title_sort |
analytic capacity, rectifiability, menger curvature and the cauchy integral [electronic resource] / |
| publisher |
Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, |
| publishDate |
2002 |
| url |
http://dx.doi.org/10.1007/b84244 |
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AT pajotherveauthor analyticcapacityrectifiabilitymengercurvatureandthecauchyintegralelectronicresource AT springerlinkonlineservice analyticcapacityrectifiabilitymengercurvatureandthecauchyintegralelectronicresource |
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1756270609414750208 |