Using contemporary concepts, this book describes the interaction between Dirichlet series and holomorphic functions in high dimensions.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Andreas Defant is Professor of Mathematics at Carl V. Ossietzky Universität Oldenburg, Germany.
Inhaltsangabe
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.
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.
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