学术报告
History and tendencies of hypercomplex analysis - Professor Sproessig Wolfgang（Technical University Bergakademie Freiberg, Germany）
题目：History and tendencies of hypercomplex analysis
报告人：Professor Sproessig Wolfgang（Technical University Bergakademie Freiberg, Germany）
摘要：Hypercomplex analysis can be seen as some kind of "`complex function theory"' for higher dimensions, where complex numbers are replaced by quaternions, coquaternions, split quaternions, Clifford numbers, octonions, sedenions etc.. Hyperholomorphic functions play the role of holomophic functions of the complex function theory in the plane. They are zero solutions of higher-dimensional versions of Cauchy-Riemann equations (Riesz system, Fueter system, system of Moisil-Teodorescu, etc.). In this talk we reduce our considerations to quaternion valued functions over 3D-domains. As in the classical function theory also in higher dimensional versions some operators are important: Dirac operator, Teodorescu transform, Cauchy-Fueter operator as well as the orthoprojections on the Bergman space of the Hilbert space (module) and on its complement. For boundary value problems we also need so-called projections of Plemelj type which are connected with the Cauchy-Fueter operator. We use and derive analog of basic theorems of the plane function theory. Using Bergman-Hodge decompositions boundary value problems can be considered. In this talk will be magnetic fluid flow and shallow water problems in the focus of applications. Further results belonging to Appell polynomials, hypercomplex parabolic Dirac operators, Dunkl operators, generalized Eisenstein series, Clifford transform analysis, spaces of holomorphic functions, etc.. are shortly explained.
时间：11月16日（周四）下午4:00-5:00
地点：首师大校本部新教二楼527
欢迎全体师生积极参加！
