報告人：Uwe Kaehler教授(阿威羅大學(xué))
題目：Higher-dimensional discrete operator theory and its applications
日期：2023年4月21日
時間：14:00-16:00 (北京時間)
騰訊會議ID：926-148-212,，Pin:1234
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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教授簡介：葡萄牙Aveiro大學(xué)數(shù)學(xué)系教授。1998/09于德國Chemnitz University of Technology數(shù)學(xué)系獲得博士學(xué)位,；2006/01于葡萄牙Aveiro大學(xué)數(shù)學(xué)系獲得Habilitation高級學(xué)術(shù)資格(歐洲國家第二階段博士),。研究領(lǐng)域為：Clifford分析及應(yīng)用,、PDE,、算子理論,、逼近論、離散函數(shù)論,、調(diào)和分析。擔(dān)任六個國際雜志編委(Complex Anal. and Operator Th., Applied Math. and Comp., Central European J. of Math., Open Math., Advances in Applied Clifford Algebras, IJWMIP),共發(fā)表論文102篇,。 現(xiàn)任ISSAC主席,。  

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