报 告 人：Jasson Vindas 副教授
Complex Tauberian theorems have been strikingly useful tools in diverse areas of mathematics such as number theory and spectral theory for differential operators. Many results in the area from the last three decades have been motivated by applications in operator theory and semigroups.
In this talk we shall discuss some developments in complex Tauberian theory for Laplace transforms. We will focus on two groups of statements, usually labeled as Ingham-Karamata theorems and Wiener-Ikehara theorems. We will present sharp versions of such theorems, including results with minimal boundary requirements on the Laplace transforms and computation of optimal Tauberian constants. Several classical applications will be discussed in order to explain the nature of these Tauberian theorems.