
Dirichlet Series and Holomorphic Functions in High Dimensions
- English
- PDF
- Available on iOS & Android
Dirichlet Series and Holomorphic Functions in High Dimensions
About this book
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.
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Information
Table of contents
- Cover
- Half-title
- Series information
- Title page
- Copyright information
- Contents
- Introduction
- PART ONE BOHR’S PROBLEM AND COMPLEX ANALYSIS ON POLYDISCS
- PART TWO ADVANCED TOOLBOX
- PART THREE REPLACING POLYDISCS BYOTHER BALLS
- PART FOUR VECTOR-VALUED ASPECTS
- References
- Symbol Index
- Subject Index