Dirichlet Series and Holomorphic Functions in High Dimensions (Hardcover)

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.