Book contents
- Frontmatter
- Contents
- Introduction
- Part 1 Bohr’s Problem and Complex Analysis on Polydiscs
- Part 2 Advanced Toolbox
- Part 3 Replacing Polydiscs by Other Balls
- Part 4 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
- Symbol Index
- Subject Index
26 - Bohr’s Problem for Vector-Valued Dirichlet Series
from Part 4 - Vector-Valued Aspects
Published online by Cambridge University Press: 19 July 2019
Book contents
- Frontmatter
- Contents
- Introduction
- Part 1 Bohr’s Problem and Complex Analysis on Polydiscs
- Part 2 Advanced Toolbox
- Part 3 Replacing Polydiscs by Other Balls
- Part 4 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
- Symbol Index
- Subject Index
Summary
The text is closed by coming back to Bohr’s absolute convergence problem, this time for vector-valued Dirichlet series. For a Banach space X abscissas and strips S(X) and S_p(X), analogous to those defined in Chapters 1 and 12 are considered. It is shown that all these strips equal 1-1/cot(X), where cot(X) is the optimal cotype of X.
Keywords
- Type
- Chapter
- Information
- Dirichlet Series and Holomorphic Functions in High Dimensions , pp. 645 - 663Publisher: Cambridge University PressPrint publication year: 2019