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Vitushkin's Conjecture for Removable Sets
Vitushkin'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. Chapter...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer New York : Imprint: Springer,
2010.
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| Edición: | 1st ed. 2010. |
| Colección: | Universitext,
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| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 001 | 978-1-4419-6709-1 | ||
| 003 | DE-He213 | ||
| 005 | 20220120082128.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 110201s2010 xxu| s |||| 0|eng d | ||
| 020 | |a 9781441967091 |9 978-1-4419-6709-1 | ||
| 024 | 7 | |a 10.1007/978-1-4419-6709-1 |2 doi | |
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| 100 | 1 | |a Dudziak, James. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Vitushkin's Conjecture for Removable Sets |h [electronic resource] / |c by James Dudziak. |
| 250 | |a 1st ed. 2010. | ||
| 264 | 1 | |a New York, NY : |b Springer New York : |b Imprint: Springer, |c 2010. | |
| 300 | |a XII, 332 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 338 | |a online resource |b cr |2 rdacarrier | ||
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| 490 | 1 | |a Universitext, |x 2191-6675 | |
| 505 | 0 | |a Removable 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 | |a Vitushkin'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 | |a Functions of complex variables. | |
| 650 | 1 | 4 | |a Functions of a Complex Variable. |
| 650 | 2 | 4 | |a Several Complex Variables and Analytic Spaces. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9781441967084 |
| 776 | 0 | 8 | |i Printed edition: |z 9781441967107 |
| 830 | 0 | |a Universitext, |x 2191-6675 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-1-4419-6709-1 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||