Dirichlet Series and Holomorphic Functions in High Dimensions 1st Edition by Andreas, Domingo, Manuel, Pablo  1108476716 9781108476713

Instant download Dirichlet Series and Holomorphic Functions in High Dimensions pdf, docx, kindle format all chapters after payment. ISBN(s): 1108476716, 9781108476713

Product details:

• ISBN-10 ‏ : ‎ 1108476716
• ISBN-13 ‏ : ‎ 9781108476713
• Author: Andreas, Domingo, Manuel, Pablo 

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.

Table of contents:

The Absolute Convergence Problem

Holomorphic Functions on Polydiscs

Bohrs Vision

Solution to the Problem

The Fourier Analysis Point of View

Inequalities I

Probabilistic Tools I

Multidimensional Bohr Radii

Strips under the Microscope

Monomial Convergence of Holomorphic Functions

Hardy Spaces of Dirichlet Series

Bohrs Problem in Hardy Spaces

Hardy Spaces and Holomorphy

Selected Topics on Banach Space Theory

Infinite Dimensional Holomorphy

Tensor Products

Probabilistic Tools II

HardyLittlewood Inequality

Bohr Radii in lp Spaces and Unconditionality

Monomial Convergence in Banach Sequence Spaces

Dineens Problem

Back to Bohr Radii

Functions of One Variable

VectorValued Hardy Spaces

Inequalities IV

Bohrs Problem for VectorValued Dirichlet Series

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