Description 
1 online resource (367 pages) : illustrations 
Series 
London Mathematical Society lecture note series ; 128 

London Mathematical Society lecture note series ; 128.

Contents 
Cover; Title; Copyright; Dedication; Preface; Contents; INTRODUCTION; ABOUT THIS BOOK; CHAPTER I. TRIGONOMETRIC SERIES AND SETS OF UNIQUENESS; 1. Trigonometric and Fourier Series; 2. The problem of uniqueness; 3. The Riemann theory and the Cantor Uniqueness Theorem; 4. The Rajchman multiplication theory. Examples of perfect sets of uniqueness; 5. Countable unions of closed sets of uniqueness; 6. Four classical problems; CHAPTER II. THE ALGEBRA A OF FUNCTIONS WITH ABSOLUTELY CONVERGENT FOURIER SERIES, PSEUDOFUNCTIONS AND PSEUDOMEASURES; 1. The spaces PF, A and PM; 2. Some basic facts about A 

3. Supports of pseudomeasures4. Description of closed 'Usets in terms of pseudofunctions; 5. Rajchman measures and extended uniqueness sets; CHAPTER III. SYMMETRIC PERFECT SETS AND THE SALEMZYGMUND THEOREM; 1. H(n)sets; 2. Pisot numbers; 3. Symmetric and homogeneous perfect sets; 4. The SalemZygmund Theorem; CHAPTER IV. CLASSIFICATION OF THE COMPLEXITY OF U; 1. Some descriptive set theory; 2. The theorem of Solovay and Kaufman; 3. On crideals of closed sets in compact, metrizable spaces; CHAPTER V. THE PIATETSKISHAPIRO HIERARCHY OF USETS; 1. IlJranks on Il{ sets 

2. Ranks for subspaces of Banach spaces3. The treerank and the Rrank; 4. The PiatetskiShapiro rank on U; 5. The class U' of uniqueness sets of rank 1; CHAPTER VI. DECOMPOSING USETS INTO SIMPLER SETS; 1. Borel bases for aideals of closed sets; 2. The class l̂ and the decomposition theorem of PiatetskiShapiro; 3. The Borel Basis Problem for U and relations between U, Ux and Uo; CHAPTER VII. THE SHRINKING METHOD, THE THEOREM OF KORNER AND KAUFMAN, AND THE SOLUTION TO THE BOREL BASIS PROBLEM FOR U; 1. Sets of interior uniqueness; 2. Approximating Msets by Hasets 

3. Helson sets of multiplicity4. The solution to the Borel Basis Problem; CHAPTER VIII. EXTENDED UNIQUENESS SETS; 1. The class U'o; 2. The existence of a Borel basis for Uo and its associated rank; 3. The solution to the Category Problem, and other applications; 4. The class Vl revisited; CHAPTER IX. CHARACTERIZING RAJCHMAN MEASURES; 1. A theorem of Mokobodzki in measure theory; 2. Wsets and Lyons* characterization of Rajchman measures; CHAPTER X. SETS OF RESOLUTION AND SYNTHESIS; 1. Sets of resolution; 2. Sets of synthesis; LIST OF PROBLEMS; REFERENCES; SYMBOLS AND ABBREVIATIONS; INDEX 
Summary 
The study of sets of uniqueness for trigonometric series has a long history, originating in the work of Riemann, Heine, and Cantor in the midnineteenth 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 selfcontained and will make an excellent introduction to the subject for graduate students and research workers in set theory and analysis 
Bibliography 
Includes bibliographical references (pages 353358) and index 
Notes 
Print version record 
Subject 
Descriptive set theory.


Fourier series.


MATHEMATICS  Infinity.


Descriptive set theory


Fourier series


Deskriptive Mengenlehre


Eindeutigkeit


Trigonometrische Reihe


Ensembles, Théorie descriptive des.


Fourier, Séries de.


Théorèmes d'unicité.

Form 
Electronic book

Author 
Louveau, Alain

ISBN 
9781107361492 

1107361494 
