题目:分析中微分和积分的代数研究
主讲人:高兴 教授
时间:2019年6月26日下午3:00
地点:3号报告厅
内容简介:
In this talk, weintroduce the integro-differential algebras, which is the simultaneousalgebraization of both integral an differential operators in analysis, startedat the algebraic approach to initial/boundary value problems of differential equationsof Rosenkranz et al. in 2008. An integro-differential algebra of weight zeroand arbitrary characteristic is given the structure of a uniform topologicalspace, such that the ring operations as well as the derivation (= differentiationoperator) and Rota-Baxter operator (= integral operator) are uniformlycontinuous.This allows one to introduce a compositionfor (topologically) complete integro-differential algebras, and to describeexponential and logarithmic elements in a way that reflects the“integro-differential properties” known from analysis.
报告人简介:
高兴,博士,兰州大学教授。于2010年7月在兰州大学数学与统计学院获得博士学位,留校工作至今。在2015年8月至2016年8月间,在美国Rutgers大学交流访问,师从Rota-Baxter代数的国际领军人物郭锂教授。主要从事Rota-Baxter代数和代数组合等领域的研究, 在Journal ofAlgebra、Journal of Pure and Applied Algebra、J.Algebraic Combin.、Pacific J. Math.、Discrete Applied Math.等国际期刊上发表SCI学术论文近四十篇。主持数学天元基金、青年科学基金、甘肃省自然科学基金项目,曾参与国家自然科学基金项目2项和甘肃省自然科学基金项目1项,出版专著一本。
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