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 Decontamination of Pesticide Residues in the Environment by James Dudziak
Cover of the book The ASCRS Manual of Colon and Rectal Surgery by James Dudziak
Cover of the book Surgical Techniques for Kidney Cancer by James Dudziak
Cover of the book Game Theoretic Approaches for Spectrum Redistribution by James Dudziak
Cover of the book Differential Equations by James Dudziak
Cover of the book The Influence of Attention, Learning, and Motivation on Visual Search by James Dudziak
Cover of the book The Invisible Sky by James Dudziak
Cover of the book Molecular Genetics of Pediatric Orthopaedic Disorders by James Dudziak
Cover of the book Reviews of Environmental Contamination and Toxicology Volume 212 by James Dudziak
Cover of the book Diagnosis of Endometrial Biopsies and Curettings by James Dudziak
Cover of the book Managing Your Headaches by James Dudziak
Cover of the book Studies on Arthritis and Joint Disorders by James Dudziak
Cover of the book Mitochondrial Oxidative Phosphorylation by James Dudziak
Cover of the book The Organization of Critical Care by James Dudziak
Cover of the book Functional Foods and Nutraceuticals 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