Time: 2019-04-09 15：30-17：30

Venue: Room 201 Lecture Hall

Abstract:

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.