報(bào)告人：Uwe Kaehler教授(阿威羅大學(xué))
題目：Introduction to reproducing kernel Clifford-Krein modules
日期：2023年4月14日
時(shí)間：14:00-16:00 (北京時(shí)間)
騰訊會(huì)議ID：393-444-481，Pin:1234
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https://meeting.tencent.com/dm/KawHpWKd4Mtp  

摘要：TClassic hypercomplex analysis is intimately linked with elliptic operators, such as the Laplacian or the Dirac operator, and positive quadratic forms. But there are many applications like the inver[1]sion of the crystallographic X-ray transform, the study of solutions of the ultrahyperbolic Dirac operator, or machine/deep learning problems which are closely connected with indefinite quadratic forms. Among other things this is due to the possibility of the underlying Clifford algebra to have a signature (p, q) and, therefore, to be linked to Pontryagin modules instead of Hilbert modules. Although in the majority of papers Hilbert modules are being used in this context they are not the right choice as function spaces since they do not reflect the induced geometry. In this talk we are going to show that Clifford-Krein modules are naturally appearing in this context. We take a partic[1]ular look into the case of Clifford-Krein modules with reproducing kernels and discuss applications in interpolation and sampling problems.

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(jí)學(xué)術(shù)資格(歐洲國家第二階段博士),。研究領(lǐng)域?yàn)椋篊lifford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(gè)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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