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Dirichlet Series and Holomorphic Functions in High Dimensions

Dirichlet Series and Holomorphic Functions in High Dimensions

$200.00 (C)

Part of New Mathematical Monographs

  • Date Published: September 2019
  • availability: In stock
  • format: Hardback
  • isbn: 9781108476713

$ 200.00 (C)

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About the Authors
  • 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.

    • Presents a contemporary view of the theory of Dirichlet series and its interaction with infinite dimensional holomorphy
    • Provides a largely self-contained treatment
    • Will appeal to graduate students who want to study the basics of this new field, and to experts as a central resource for references
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    Reviews & endorsements

    '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, Choice

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    Product details

    • Date Published: September 2019
    • format: Hardback
    • isbn: 9781108476713
    • length: 706 pages
    • dimensions: 234 x 157 x 42 mm
    • weight: 1.14kg
    • contains: 3 b/w illus.
    • availability: In stock
  • Table of Contents

    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
    List of symbols
    Subject index.

  • Authors

    Andreas Defant, Carl V. Ossietzky Universität Oldenburg, Germany
    Andreas Defant is Professor of Mathematics at Carl V. Ossietzky Universität Oldenburg, Germany.

    Domingo García, Universitat de València, Spain
    Domingo García is Professor of Mathematics at Universitat de València, Spain.

    Manuel Maestre, Universitat de València, Spain
    Manuel Maestre is Full Professor of Mathematics at Universitat de València, Spain.

    Pablo Sevilla-Peris, Universitat Politècnica de València, Spain
    Pablo Sevilla-Peris is Associate Professor of Mathematics at Universitat Politècnica de València, Spain.

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