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Descriptive Set Theory and the Structure of Sets of Uniqueness : ICMI Study Series - A. S. Kechris

Descriptive Set Theory and the Structure of Sets of Uniqueness

ICMI Study Series

Paperback Published: 6th June 1988
ISBN: 9780521358118
Number Of Pages: 380

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The study of sets of uniqueness for trigonometric series has a long history, originating in the work of Riemann, Heine, and Cantor in the mid-nineteenth century. Since then it has been a fertile ground for numerous investigations involving real analysis, classical and abstract harmonic analysis, measure theory, functional analysis and number theory. In this book are developed the intriguing and surprising connections that the subject has with descriptive set theory. These have only been discovered recently and the authors present here this novel theory which leads to many new results concerning the structure of sets of uniqueness and include solutions to some of the classical problems in this area. In order to make the material accessible to logicians, set theorists and analysts, the authors have covered in some detail large parts of the classical and modern theory of sets of uniqueness as well as the relevant parts of descriptive set theory. Thus the book is essentially self-contained and will make an excellent introduction to the subject for graduate students and research workers in set theory and analysis.

"Of all the work that has been done in recent years on connections between descriptive set theory and analysis, the results contained in this book are the deepest and most significant." Mathematical Reviews

Introduction
About this book
Trigonometric series and sets of uniqueness
The algebra A of functions with absolutely convergent fourier series, pseudofunctions and pseudomeasures
Symmetric perfect sets and the Salem-Zygmund theorem
Classification of the complexity of U
The Piatetski-Shapiro hierarchy of U-sets
Decomposing U-sets into simpler sets
The shrinking method, the theorem of K├Ěrner and Kaufman, and the solution to the Borel basis problem for U
Extended uniqueness sets
Characterizing Rajchman measures
Sets of resolution and synthesis
List of problems
References
Symbols and Abbreviations
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521358118
ISBN-10: 0521358116
Series: ICMI Study Series
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 380
Published: 6th June 1988
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 2.16
Weight (kg): 0.55