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Diophantine Approximation and Dirichlet Series

Part of the Texts and Readings in Mathematics Book Series (volume 80)

DOI: 10.1007/978-981-15-9351-2

ISBN: 978-981-15-9350-5

Publisher: Springer Singapore - Springer Journals

Jan 28, 2021

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Chapter 1A Review of Commutative Harmonic Analysis

Queffelec, Hervé; Queffelec, Martine

Pages: 1 –36

[This chapter might be skipped at first reading. But we have the feeling that a minimal knowledge of basic facts in harmonic analysis is necessary to understand certain aspects of the analytic theory of Dirichlet seriesDirichletseries, especially those connected with almost-periodicity, ergodic...
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Chapter 2Ergodic Theory and Kronecker’s Theorems

Queffélec, Hervé; Queffélec, Martine

Pages: 37 –67

[Measure theory, sometimes, brings out the existence of specific elements by giving a positive measure to the set of such objects. For want of anything better, it can also be used in the number-theoretical framework to produce classifications of real numbers through their expansions. Ergodic...
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Chapter 3Diophantine Approximation

Queffélec, Hervé; Queffélec, Martine

Pages: 69 –94

[Throughout this chapter, [x] denotes the integral part and {x}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
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Chapter 4General Properties of Dirichlet Series

Queffélec, Hervé; Queffélec, Martine

Pages: 95 –127

[For a real number θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta...
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Chapter 5Probabilistic Methods for Dirichlet Series

Queffélec, Hervé; Queffélec, Martine

Pages: 129 –143

[The title of this chapter is a little emphatic, because the probabilistic methods will here concentrate essentially on one maximal inequality, which is fairly well-known in harmonic analysis, but will have a specific aspect, due to the BohrBohr point of viewBohrpoint of view on Dirichlet series.]
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Chapter 6Hardy Spaces of Dirichlet Series

Queffélec, Hervé; Queffélec, Martine

Pages: 145 –196

[The forthcoming spaces Hp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...
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Chapter 7Voronin-Type Theorems

Queffélec, Hervé; Queffélec, Martine

Pages: 197 –236

[In thisL-function introductory section, we begin by fixing some notations, recalling some basic facts on Dirichlet charactersDirichletcharacter [1, Chap. 5] and presenting the main results to be discussed. The techniques (Hilbertian spaces of analytic functions, ergodic theorems) are a good...
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Chapter 8Composition Operators on the Space H2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {H}^2$$\end{document} of Dirichlet Series

Queffélec, Hervé; Queffélec, Martine

Pages: 237 –281

[The general framework for composition operators acting on a Banach space X of functions analytic on a domain Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...

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