报告名称：Monogenic signals on unit ball via Riemann-Hilbert problems

主办单位：数学与统计学学院

报告专家：库敏 博士后

专家所在单位：University of Aveiro

报告时间：2019年4月9日15:30-17:30

报告地点：数学与统计学学院203会议室

报告摘要：While it is well-known that to reconstruct analytic signals could be equal to solve a Riemann-Hilbert problem for Hardy spaces in the plane, there is not much known about the case of monogenic signals in three dimensions up to now. Our motivation is to reconstruct monogenic signals in terms of the study of Riemann-Hilbert boundary value problems for Hardy spaces in higher dimensional space. In this talk, we mainly focus on our recent work about the Riemann-Hilbert boundary value problems for poly-Hardy spaces on the unit ball of higher dimensional Euclidean space. As a special case, monogenic signals for Hardy space on the unit sphere will be reconstructed when the boundary data are given, which is the generalization of analytic signals for Hardy space on the unit circle of complex plane. We discuss the boundary behavior of functions in the poly-Hardy class, construct the Schwarz kernel function and the higher order Schwarz operator to study the Riemann-Hilbert boundary value problems for Hardy class and poly-Hardy class on the unit ball of higher dimensions, and obtain the expressions of solutions explicitly.