报告人：Uwe Kaehler教授(阿威罗大学)
题目：Higher-dimensional discrete operator theory and its applications
日期：2023年4月21日
时间：14:00-16:00 (北京时间)
腾讯会议ID：926-148-212，Pin:1234
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https://meeting.tencent.com/dm/nU73dFdvLQ8g
摘要：In the last two decades one can observe an increasing interest in function and operator theories of discrete structures. This increasing interest is based on the one hand in the fact that increased computational power is nowadays available to everybody and that computers can essentially work only with discrete values. This is true even for topics which are originally unrelated to the field, like the Ising model in statistical physics, finite element exterior calculus, or machine learning problems. This means that one requires discrete structures which are equivalent to the usual continuous structures. But while there exists a long history of discrete function and operator theories in the two-dimensional case, unfortunately, this is not true in the higher dimensional case which is being developed in earnest only since the 1980s. In this talk we will present the basic ingredients of a discrete function and operator theory. This not only includes a theory of discrete boundary values, discrete Hilbert/Riesz-transforms, and Hardy spaces, but also discrete pseudo-differential operators and highlight the differences to the continuous case. Among possible applications we are going to discuss discrete Riemann boundary value problems and their importance for image processing.
Uwe Kaehler教授简介：葡萄牙Aveiro大学数学系教授。1998/09于德国Chemnitz University of Technology数学系获得博士学位；2006/01于葡萄牙Aveiro大学数学系获得Habilitation高级学术资格(欧洲国家第二阶段博士)。研究领域为：Clifford分析及应用、PDE、算子理论、逼近论、离散函数论、调和分析。担任六个国际杂志编委(Complex Anal. and Operator Th., Applied Math. and Comp., Central European J. of Math., Open Math., Advances in Applied Clifford Algebras, IJWMIP),共发表论文102篇。 现任ISSAC主席。
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