关于举行朱永昌教授（香港科技大学）学术报告会的通知

报告主题: Variation Diminishing Operators and Unitary Representations SL(2) over Semifields

报 告人: 朱永昌教授（香港科技大学）

报告时间：2023年07月13日（星期四）上午10:00-11:00

报告地点：四号楼4224

邀 请人: 刘明副教授、常智华副教授

欢迎广大师生前往！

数学学院

2023年07月13日

报告摘要：In this talk we study unitary representations of SL(2) over semifield of positive real numbers and over tropical semifield of positive real numbers. We introduce the concept of unitary representations and classify irreducible ones. And we give explicit models of the irreducible representations on functions space over half line and show that the elements in SL(2) act as variation diminishing operators and preserve the nonnegative functions. That is, the infinite matrices for these operators are totally positive. The proof uses the results of Schoenberg and Hirschman about variation diminishing operators.