Descriptive Set Theory and the Structure of Sets of Uniqueness

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The authors present some surprising connections that sets of uniqueness for trigonometic series have with descriptive set theory. They present many new results concerning the structure of sets of uniqueness and include solutions to some of the classical problems in this area. Topics covered include symmetric perfect sets and the solution to the Borel Basis Problem for U, the class of sets of uniqueness. To make the material accessible to both 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. Because the book is essentially selfcontained and requires the minimum prerequisites, it will serve as an excellent introduction to the subject for graduate students and research workers in set theory and analysis.

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Editorial Reviews

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"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
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Product Details

Table of Contents

Introduction; About this book; 1. Trigonometric series and sets of uniqueness; 2. The algebra A of functions with absolutely convergent fourier series, pseudofunctions and pseudomeasures; 3. Symmetric perfect sets and the Salem-Zygmund theorem; 4. Classification of the complexity of U; 5. The Piatetski-Shapiro hierarchy of U-sets; 6. Decomposing U-sets into simpler sets; 7. The shrinking method, the theorem of K├Ârner and Kaufman, and the solution to the Borel basis problem for U; 8. Extended uniqueness sets; 9. Characterizing Rajchman measures; 10. Sets of resolution and synthesis; List of problems; References; Symbols and Abbreviations; Index.

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