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Analytic Capacity, Rectifiability, Menger Curvature and the Cauchy Integral / by Hervé Pajot.
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View onlineMath/Physics/Astronomy Library QA3 .L28 v.1-999 470,523,830,849:2nd ed. v.1000-1722,1762,1781,1799-2099,2100-2192-2218 2219-2223-2258,2260-2271,2273-2274-2277,2279-2281,2283-2289,2291,2293-2294,2296,2298-2299,2300-2311,2313-2379,2381-2384 2385-2386,2388-2389
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LIBRA QA3 .L28 Scattered vols.
Mixed Availability
- Format:
- Book
- Author/Creator:
- Pajot, Hervé, 1967- author.
- Series:
- Lecture Notes in Mathematics, 0075-8434 ; 1799.
- Lecture Notes in Mathematics, 0075-8434 ; 1799
- Language:
- English
- Subjects (All):
- Global analysis (Mathematics).
- Geometry.
- Mathematics.
- Functions of complex variables.
- Fourier analysis.
- Analysis.
- Measure and Integration.
- Functions of a Complex Variable.
- Fourier Analysis.
- Local Subjects:
- Analysis.
- Geometry.
- Measure and Integration.
- Functions of a Complex Variable.
- Fourier Analysis.
- Physical Description:
- 1 online resource (VIII, 119 pages).
- Contained In:
- Springer eBooks
- Place of Publication:
- Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.
- System Details:
- text file PDF
- Summary:
- 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.
- Contents:
- 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.
- Other Format:
- Printed edition:
- ISBN:
- 9783540360742
- Access Restriction:
- Restricted for use by site license.
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