Dirichlet Series and their Banach Spaces

Abstract: In the first half of this lecture, we will talk about the basic properties of Dirichlet series, the different convergence abscissas of a Dirichlet Series, comparisons of Dirichlet series with power series of analytic functions, and also briefly understand Bohr's point of view of identifying a Dirichlet polynomial with a polynomial on some polydisk. In the second half, we will talk about the Hardy spaces of Dirichlet series, two inequalities of Bohr, and try to understand the fundamental question asked by Bohr about the convergence abscissas of a Dirichlet series.

Host: Christopher Felder