115周年校庆“学术Beoplay 中国官网”系列活动之0109:数信学院系列讲座GROTHENDIECK-LIDSKII FORMULAE IN HYPERCOMPLEX ANALYSIS

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:2024-04-30

Add: 483 Wushan Road, Tianhe district, Guangzhou, P.R.China

Website: http://www.scau.edu.cn

Postal Code: 510642


Beoplay 中国官网数信学院系列讲座

报告人:Uwe Kaehler教授(阿威罗大学)

题目一:  GROTHENDIECK-LIDSKII FORMULAE IN HYPERCOMPLEX ANALYSIS

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时间:9:30-11:00(北京时间)

地点:数学与信息学院西楼605

摘要: The classic Grothendieck-Lidskii formula provides a connection between the trace and Fredholm determinant and the spectrum of a Fredholm operator. Unfortunately, linear algebra over non-commutative structures like Quaternions and Clifford algebras is quite different from classic linear algebra and, consequently, the classic formula does not hold in this case. In this talk we will discuss the difficulties and

show how a type of Grothendieck-Lidskii formula can be established in these cases.

题目二Triangular decompositions of quaternionic non-self-adjoint operators

日期:2024715

时间:11:00-12:30(北京时间)

摘要: One of the principal problems in studying spectral theory for quaternionic or Clifford-algebra-valued operators lies in the fact that due to the noncommutativity many methods from classic spectral theory are not working anymore in this setting. For instance, even in the simplest case of finite rank operators there are different notions of a left and right spectrum. Hereby, the notion of a left spectrum has little practical use while the notion of a right spectrum is based on a nonlinear eigenvalue problem. In the present talk we will recall the notion of S-spectrum as a natural way to consider a spectrum in a noncommutative setting and use it to study quaternionic non-selfadjoint operators. To this end we will discuss quaternionic Volterra operators and triangular representation of quaternionic operators similar to the classic approaches by Gohberg, Krein, Livsic, Brodskii and de Branges. Hereby we introduce spectral integral representations with respect to quaternionic chains and discuss the concept of P- triangular operators in the quaternionic setting. This will allow us to study the localization of spectra of non-selfadjoint quaternionic operators and presented triangular decompositions of non-selfadjoint operators with respect to maximal quaternionic eigenchains.

 

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Advances in Applied Clifford Algebras主编,以下国际杂志编委(Complex Anal. and Operator Th. Applied Math. and Comp. Central European J. of Math. Open Math. IJWMIP。 共发表科研论文一百多篇。


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