Vitushkin’s Conjecture for Removable Sets

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis
Cover of the book Vitushkin’s Conjecture for Removable Sets by James Dudziak, Springer New York
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: James Dudziak ISBN: 9781441967091
Publisher: Springer New York Publication: February 3, 2011
Imprint: Springer Language: English
Author: James Dudziak
ISBN: 9781441967091
Publisher: Springer New York
Publication: February 3, 2011
Imprint: Springer
Language: English

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 1-5 of the 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. 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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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 1-5 of the 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. 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.

More books from Springer New York

Cover of the book The Archaeology of Watercraft Abandonment by James Dudziak
Cover of the book Looming Vulnerability by James Dudziak
Cover of the book Robotized Transcranial Magnetic Stimulation by James Dudziak
Cover of the book Theoretical Principles of Sociology, Volume 1 by James Dudziak
Cover of the book Advances in Fetal and Neonatal Physiology by James Dudziak
Cover of the book Residue Reviews by James Dudziak
Cover of the book Cardiothoracic Surgery in the Elderly by James Dudziak
Cover of the book Historical Archaeology of Gendered Lives by James Dudziak
Cover of the book Reforms in Long-Term Care Policies in Europe by James Dudziak
Cover of the book Educational Media and Technology Yearbook by James Dudziak
Cover of the book Genomics Applications for the Developing World by James Dudziak
Cover of the book Proteases in Health and Disease by James Dudziak
Cover of the book Dynamic-Mismatch Mapping for Digitally-Assisted DACs by James Dudziak
Cover of the book Evolution of Gibbons and Siamang by James Dudziak
Cover of the book Phenotyping for Plant Breeding by James Dudziak
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy