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20140310151444.0 |
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110201s2010 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
9781441967091 |
|
978-1-4419-6709-1 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA331.7 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
515.94 |
| Edition number |
23 |
| 264 #1 - |
|---|
| -- |
New York, NY : |
| -- |
Springer New York : |
| -- |
Imprint: Springer, |
| -- |
2010. |
| 912 ## - |
|---|
| -- |
ZDB-2-SMA |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Dudziak, James J. |
| Relator term |
author. |
| 245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE |
|---|
| Title |
Vitushkin’s Conjecture for Removable Sets |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc |
by James J. Dudziak. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
XII, 272p. |
| Other physical details |
online resource. |
| 440 1# - SERIES STATEMENT/ADDED ENTRY--TITLE |
|---|
| Title |
Universitext, |
| International Standard Serial Number |
0172-5939 |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
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 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
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 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Differential equations, partial. |
|
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Several Complex Variables and Analytic Spaces. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
|---|
| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
|---|
| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Display text |
Printed edition: |
| International Standard Book Number |
9781441967084 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-1-4419-6709-1 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
|
| Item type |
E-Book |
