Dirichlet Series and Holomorphic Functions in High Dimensions (New Mathematical Monographs)

Description

Over 100 years ago Harald Bohr identified a deep problem about the convergence of Dirichlet series. In recent years there has been a substantial revival of interest in this topic, and the goal of this book is to describe in detail some of its key elements to a wide audience. Cover Front Matter NEW MATHEMATICAL MONOGRAPHS Dirichlet Series and Holomorphic Functions in High Dimensions Copyright Contents Introduction PART ONE: 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 TWO: ADVANCED TOOLBOX 14 Selected Topics on Banach Space Theory 15 Infinite Dimensional Holomorphy 16 Tensor Products 17 Probabilistic Tools II PART THREE: 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 FOUR: 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 Symbol Index Subject Index