Mayya Golitsyna (UCD)

will speak on

Overconvergence Properties of Dirichlet series

Time: 3:00PM
Date: Tue 16th October 2018
Location: Seminar Room SCN 1.25 [map]

Abstract: In this talk we discuss the properties of the subsequences of the partial sums of general Dirichlet series. It is known that a Dirichlet series of the form $\sum_{j=0}^\infty a_je^{-\lambda_js}$ either diverges, converges on some half-plane $\{\mathrm{Re}(s)>c\}$ to a holomorphic function $f$ or converges on the whole complex plane. In case where the series converges on a half-plane it is possible that the function $f$ has a holomorphic extension to a larger domain that strictly contains the half-plane. We will give sufficient conditions for a subsequence of partial sums of the series to converge at every regular point of $f.$
We apply potential theoretic techniques to prove the results.

(This talk is part of the Analysis series.)

PDF notice

Return to all seminars