报告题目：Discrete Dirac operator and harmonic analysis

报告人：Uwe Kahler副教授， 葡萄牙阿维罗大学数学系

报告时间： 2013年6月24日  星期一   4：00-5：00pm

报告地点： 管理科研楼1518教室

摘要：There is a growing interest in extending results from continuous to discrete Analysis. On one hand due to the availability of large computational power to everyone one can see a shift from classic continuous modeling to a more direct discrete modeling. One example is the shift in the basic philosophy of the Finite Element Method by the introduction of nite element exterior calculus and the discussion of variational crimes. On the other hand quantized problems are becoming more and more important in physics where complex systems are directly studied at the discrete level. This can be observed, among others, by recent results of S. Smirnov in connecting complex discrete function theory with problems in statistical physics, like the 2D-Ising model. Such a shift of paradigm also requires the development of discrete function theories in higher dimensions, one of them being the so-called discrete Cliord analysis. Discrete Cliord analysis started eectively only in the eighties and nineties with the construction of discrete Dirac operators either for numerical methods of partial dierential equations or for quantized problems in physics with its development as a discrete counterpart to classic Cliord analysis being even more recent. The development of Discrete Clifford analysis as being a discrete counterpart to classic Cliord analysis only started quite recently. In this talk we would like to discuss the possibility to use methods from harmonic analysis, particularly phase-space analysis to construct discrete function theories in higher dimensions. In this talk we would like to present the necessary methods for constructing discrete function theories, such as basic algebraic structures, Fischer decomposition, and decomposition theorems for discrete monogenic functions. We will pay special attention to the usefulness of classic harmonic analysis method in this context and its adaptations, such as the Sommen-Weyl algebra.

主办单位:  中国科学技术大学数学科学学院          中科院吴文俊数学重点实验室

 
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