Analytic Capacity, the Cauchy Transform, and Non-homogeneous Calderón–Zygmund Theory (Record no. 92498)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03823nam a22004815i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-319-00596-6 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20140220082506.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 131216s2014 gw | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783319005966 |
| -- | 978-3-319-00596-6 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-319-00596-6 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA331-355 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBKD |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT034000 |
| Source | bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515.9 |
| Edition number | 23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Tolsa, Xavier. |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Analytic Capacity, the Cauchy Transform, and Non-homogeneous Calderón–Zygmund Theory |
| Medium | [electronic resource] / |
| Statement of responsibility, etc | by Xavier Tolsa. |
| 264 #1 - | |
| -- | Cham : |
| -- | Springer International Publishing : |
| -- | Imprint: Birkhäuser, |
| -- | 2014. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | XIII, 396 p. 8 illus. |
| Other physical details | online resource. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| 490 1# - SERIES STATEMENT | |
| Series statement | Progress in Mathematics, |
| International Standard Serial Number | 0743-1643 ; |
| Volume number/sequential designation | 307 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Introduction -- Basic notation -- Chapter 1. Analytic capacity -- Chapter 2. Basic Calderón-Zygmund theory with non doubling measures -- Chapter 3. The Cauchy transform and Menger curvature -- Chapter 4. The capacity γ+ -- Chapter 5. A Tb theorem of Nazarov, Treil and Volberg -- Chapter 6. The comparability between γ and γ +, and the semiadditivity of analytic capacity -- Chapter 7. Curvature and rectifiability -- Chapter 8. Principal values for the Cauchy transform and rectifiability -- Chapter 9. RBMO(μ) and H1 atb(μ) -- Bibliography -- Index. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | This book studies some of the groundbreaking advances that have been made regarding analytic capacity and its relationship to rectifiability in the decade 1995–2005. The Cauchy transform plays a fundamental role in this area and is accordingly one of the main subjects covered. Another important topic, which may be of independent interest for many analysts, is the so-called non-homogeneous Calderón-Zygmund theory, the development of which has been largely motivated by the problems arising in connection with analytic capacity. The Painlevé problem, which was first posed around 1900, consists in finding a description of the removable singularities for bounded analytic functions in metric and geometric terms. Analytic capacity is a key tool in the study of this problem. In the 1960s Vitushkin conjectured that the removable sets which have finite length coincide with those which are purely unrectifiable. Moreover, because of the applications to the theory of uniform rational approximation, he posed the question as to whether analytic capacity is semiadditive. This work presents full proofs of Vitushkin’s conjecture and of the semiadditivity of analytic capacity, both of which remained open problems until very recently. Other related questions are also discussed, such as the relationship between rectifiability and the existence of principal values for the Cauchy transforms and other singular integrals. The book is largely self-contained and should be accessible for graduate students in analysis, as well as a valuable resource for researchers. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Functions of complex variables. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Potential theory (Mathematics). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematical optimization. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Functions of a Complex Variable. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Potential Theory. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Calculus of Variations and Optimal Control; Optimization. |
| 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 | 9783319005959 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Progress in Mathematics, |
| -- | 0743-1643 ; |
| Volume number/sequential designation | 307 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://dx.doi.org/10.1007/978-3-319-00596-6 |
| 912 ## - | |
| -- | ZDB-2-SMA |
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