数信系列讲座(二):Introduction to reproducing kernel Clifford-Krein modules

来源单位及审核人:编辑:审核发布:数学与信息学院 发布时间:2023-04-06浏览次数:77

报告人:Uwe Kaehler教授(阿威罗大学)
题目:Introduction to reproducing kernel Clifford-Krein modules
日期:2023年4月14日
时间:14:00-16:00 (北京时间)
腾讯会议ID:393-444-481,Pin:1234
点击链接入会,或添加至会议列表:
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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