題  目：Reconstruction of image via Riemann-Hilbert problems on discrete half lattices

内容簡介：The Riemann-Hilbert problem on the Hardy space is one of the classic topics in complex analysis of one complex variable. The question of finding an analytic function, whose boundary belongs to a Hardy space, by its boundary values connects to many problems in continuum mechanics, in hydrodynamics or in materials with memory. Its solvability in the framework of the classical complex analysis was studied in the classical papers of F.D. Gakhov, I.N. Vekua, N.I. Mishkelishvili, B.V. Khvedekidze, D.A. Kveselava and others. Nowadays it has been extended to three dimensional cases by making full use of the Clifford analysis. These three dimensional Riemann-Hilbert problems are linked not only to problems from the continuum mechanics, but also to other areas like the image reconstruction in three dimensional spaces, where the notion of monogenic signal corresponds to the solutions of a Riemann-Hilbert problem on a Hardy space. In this presentation, we focus on the Riemann-Hilbert problems on a Hadrdy space on half discrete lattices. We first introduce discrete monogenic functions. Then we define the corresponding Hardy spaces on half lattices. Afterwards, we derive the solutions to the Riemann-Hilbert problems in terms of the discrete Cauchy transforms for the Hardy class on the upper and lower discrete half spaces. Finally, we prove their convergence to those of the corresponding continuous Riemann-Hilbert boundary value problems.

報告人：荷蘭拉德堡德大學(University of Radboud)  庫敏  研究員

報告人簡介：荷蘭拉德堡德大學(University of Radboud)計算科學系和葡萄牙阿威羅大學(University of Aveiro)數學系雙聘研究員，是複分析和Clifford分析領域傑出的青年學者，在國際上一些重要的數學期刊上發表30多篇研究論文。

時  間：2019年5月14日（周二）下午3：00始

地  點：南海樓330室

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