Interpolation and Sidon Sets for Compact Groups

ISBN-13: 9781461453918 / Angielski / Twarda / 2013 / 249 str.

Colin C. Graham; Kathryn E. Hare

Opis

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 Englishwhich featuresa 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. "

Recenzje

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)

Spis treści

Preface .- Introduction .- Hadamard Sets.- $\epsilon$-Kronecker sets.- Sidon sets: Introduction and decomposition properties.- Characterizations of $I_0$ sets.- Proportional characterizations of Sidon sets.- Decompositions of $I_0$ sets.- Sizes of thin sets.- Sets of zero discrete harmonic density.- Related results.-Open problems.- Appendices (Groups, Probability, Combinatoric results,...).- Bibliography.- Author index.- Subject index.- Index of notation. ​