Interpolation and Sidon Sets for Compact Groups

1. Front Matter

   Pages i-xvii

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2. Hadamard Sets

   • Colin C. Graham, Kathryn E. Hare

   Pages 1-18

3. ε-Kronecker Sets

   • Colin C. Graham, Kathryn E. Hare

   Pages 19-47

4. I ₀ Sets and Their Characterizations

   • Colin C. Graham, Kathryn E. Hare

   Pages 49-66

5. More Restrictive Classes of I ₀ Sets

   • Colin C. Graham, Kathryn E. Hare

   Pages 67-76

6. Unions and Decompositions of I ₀(U) Sets

   • Colin C. Graham, Kathryn E. Hare

   Pages 77-91

7. Sidon Sets: Introduction and Decomposition Properties

   • Colin C. Graham, Kathryn E. Hare

   Pages 93-116

8. Sidon Sets Are Proportional Quasi-independent

   • Colin C. Graham, Kathryn E. Hare

   Pages 117-134

9. How Thin Are Sidon Sets in the Bohr Compactification?

   • Colin C. Graham, Kathryn E. Hare

   Pages 135-151

10. The Relationship Between Sidon and I ₀

    • Colin C. Graham, Kathryn E. Hare

    Pages 153-173

11. Sets of Zero Discrete Harmonic Density

    • Colin C. Graham, Kathryn E. Hare

    Pages 175-186

12. Interpolation and Sidon Sets for Groups That Are Not Compact and Abelian

    • Colin C. Graham, Kathryn E. Hare

    Pages 187-200

13. Combinatorial Results

    • Colin C. Graham, Kathryn E. Hare

    Pages 201-206

14. Background Material

    • Colin C. Graham, Kathryn E. Hare

    Pages 207-222

15. Back Matter

    Pages 223-249

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Understanding special sets of integers was classically of interest to Hadamard, Zygmund and others, and continues to be of interest today. This book is a modern treatment of the subject of interpolation and Sidon sets. It is a unique book, aimed at both new and experienced researchers. In particular, this is the only book in English which features a complete treatment of the Pisier-Bourgain results on Sidon sets, many of which were originally in French, in hard to access publications. Applications of the P-B results, due to Pisier, Bourgain, Ramsey, and the authors are included.    The book introduces the reader to a wealth of methods important in mathematics today: topological, probabilistic, algebraic, combinatoric and analytic. It prepares students to perform research in the area and provides both exercises and open problems. The book also provides direction to the literature for topics it does not fully cover. The book is self-contained, with appendices covering results that are required, but not necessarily in the pre-requisite background of a student ready to choose an area for research in harmonic analysis. ​

• Bohr Topology
• Interpolation Sets
• Kronecker sets
• Probablistic Methods in Harmonic Analysis
• Quasi-independent sets
• Sidon Sets

From the book reviews:

“This is … a book that puts together a great deal of deep, and at many points appealing, information that could only be found before in scattered sources. This new perspective makes the picture much more clear and will surely be welcome by experts and students. In this sense, such a contribution was necessary and the final result can only be regarded as notable.” (Jorge Galindo, Mathematical Reviews, April, 2014)

“The book under review … fills a gap in the literature and gives a complete overview of the actual state of the art. Moreover, it concerns not only Sidon sets, but more generally interpolation sets … and it is the first book on this subject. … This book is very well written, with a pedagogic concern, and very pleasant to read. The chapters end with some exercises … and very interesting historical comments and indications on connected subjects.” (Daniel Li, zbMATH, Vol. 1267, 2013)

• , Department of Mathematics, University of British Columbia, Vancouver, Canada

  Colin C. Graham

• , Department of Pure Mathematics, University of Waterloo, Waterloo, Canada

  Kathryn E. Hare

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