Vitushkin’s Conjecture for Removable Sets - Couverture souple

Dudziak, James

Couverture souple

ISBN 10 : 1441967087 ISBN 13 : 9781441967084

Editeur : Springer, 2010

Synopsis

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 arc length 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, arc length 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.

A propos du livre

À propos de l'auteur

James J. Dudziak received his Ph.D from Indiana University and is currently a visiting associate professor at Michigan State University at Lyman Briggs College. He published six excellent papers in good journals from 1984 to 1990 when he received tenure at Bucknell University.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2010
• Langue: anglais
• ISBN 10: 1441967087
• ISBN 13: 9781441967084
• Reliure: Broché
• Nombre de pages: 344
• Coordonnées du fabricant: Springer-Verlag GmbH; customerservice@springernature.com; ; Tiergartenstraße 17; Heidelberg; Baden-Württemberg; 69121; Allemagne