Dirichlet Series and Holomorphic Functions in High Dimensions
Published on 8. August 2019
Book
Hardback
706 pages
978-1-108-47671-3 (ISBN)
Description
Over 100 years ago Harald Bohr identified a deep problem about the convergence of Dirichlet series, and introduced an ingenious idea relating Dirichlet series and holomorphic functions in high dimensions. Elaborating on this work, almost twnety years later Bohnenblust and Hille solved the problem posed by Bohr. In recent years there has been a substantial revival of interest in the research area opened up by these early contributions. This involves the intertwining of the classical work with modern functional analysis, harmonic analysis, infinite dimensional holomorphy and probability theory as well as analytic number theory. New challenging research problems have crystallized and been solved in recent decades. The goal of this book is to describe in detail some of the key elements of this new research area to a wide audience. The approach is based on three pillars: Dirichlet series, infinite dimensional holomorphy and harmonic analysis.
Reviews / Votes
'Dirichlet series have been studied for well over a century and still form an integral part of analytic number theory ... The purpose of this text is to illustrate the connections between the Dirichlet series per se and the fields just mentioned, e.g., both functional and harmonic analysis ... The authors succeed in transferring important concepts and theorems of analytic function theory, in finitely many variables, to the theory in infinitely many variables.' J. T. Zerger, ChoiceMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 3 Halftones, black and white
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 46 mm
Weight
1286 gr
ISBN-13
978-1-108-47671-3 (9781108476713)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Andreas Defant | Domingo Garcia | Manuel Maestre
Dirichlet Series and Holomorphic Functions in High Dimensions
E-Book
07/2019
Cambridge University Press
€161.99
Available for download
Persons
Andreas Defant is Professor of Mathematics at Carl V. Ossietzky Universität Oldenburg, Germany.
Content
Introduction; Part I. Bohr's Problem and Complex Analysis on Polydiscs: 1. The absolute convergence problem; 2. Holomorphic functions on polydiscs; 3. Bohr's vision; 4. Solution to the problem; 5. The Fourier analysis point of view; 6. Inequalities I; 7. Probabilistic tools I; 8. Multidimensional Bohr radii; 9. Strips under the microscope; 10. Monomial convergence of holomorphic functions; 11. Hardy spaces of Dirichlet series; 12. Bohr's problem in Hardy spaces; 13. Hardy spaces and holomorphy; Part II. Advanced Toolbox: 14. Selected topics on Banach space theory; 15. Infinite dimensional holomorphy; 16. Tensor products; 17. Probabilistic tools II; Part III. Replacing Polydiscs by Other Balls: 18. Hardy-Littlewood inequality; 19. Bohr radii in lp spaces and unconditionality; 20. Monomial convergence in Banach sequence spaces; 21. Dineen's problem; 22. Back to Bohr radii; Part IV. Vector-Valued Aspects: 23. Functions of one variable; 24. Vector-valued Hardy spaces; 25. Inequalities IV; 26. Bohr's problem for vector-valued Dirichlet series; References; List of symbols; Subject index.