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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.

Approximation theory. --- Geometric analysis. --- Interpolation. --- Interpolation --- Sidon sets --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Sidon sets. --- Compact Abelian groups. --- Abelian groups, Compact --- Groups, Compact Abelian --- Sets, Sidon --- Mathematics. --- Harmonic analysis. --- Fourier analysis. --- Functional analysis. --- Abstract Harmonic Analysis. --- Fourier Analysis. --- Functional Analysis. --- Compact groups --- Topological groups --- Compact Abelian groups --- Harmonic analysis --- Set theory --- Approximation theory --- Numerical analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Analysis, Fourier --- Mathematical analysis --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis