Dirichlet Series and Holomorphic Functions in High Dimensions

Using contemporary concepts, this book describes the interaction between Dirichlet series and holomorphic functions in high dimensions.

List of contents

Introduction; 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; References; List of symbols; Subject index.

About the author

Andreas Defant is Professor of Mathematics at Carl V. Ossietzky Universität Oldenburg, Germany.Domingo García is Professor of Mathematics at Universitat de València, Spain.Manuel Maestre is Full Professor of Mathematics at Universitat de València, Spain.Pablo Sevilla-Peris is Associate Professor of Mathematics at Universitat Politècnica de València, Spain.

Summary

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.

Product details

• Authors: Andreas Defant, Andreas (Carl V. Ossietzky Universitat Old Defant, Andreas (Carl V. Ossietzky Universitat Oldenburg Defant, Defant Andreas, Domingo Garcia, Domingo (Universitat de Valencia Garcia, Domingo García, Manuel Maestre, Manuel (Universitat de Valencia Maestre, Maestre Manuel, Pablo Sevilla-Peris
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 31.08.2019
• EAN: 9781108476713
• ISBN: 978-1-108-47671-3
• No. of pages: 706
• Series: New Mathematical Monographs; New Mathematical Monographs
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; MATHEMATICS / Algebra / Abstract, Calculus & mathematical analysis, Calculus and mathematical analysis