报 告 人：刘文杰讲师 哈尔滨工业大学
报告题目：Polynomialapproximation of singular functions
报告时间：2021年5月30日（周日）上午10：10
报告地点：静远楼204学术报告厅
主办单位：数学与统计学院、科学技术研究院
报告人简介：
刘文杰，现为哈尔滨工业大学数学学院讲师。曾经为新加坡南洋理工大学的访问学者和Research Fellow。当前主要研究谱方法和谱元法求解奇异性问题、逼近理论、发展方程的数值解法等。目前主持中国博士后科学基金面上项目和国家自然科学基金青年项目。在Mathematics of Computation，Journal of Computational Physics，Journal of Approximation Theory，Journal of Scientific Computing等国际著名期刊发表SCI论文17篇。
报告摘要：
In this talk, we introduce a newtheoretical framework built upon fractional Sobolev-type spaces involvingRiemann-Liouville fractional integrals/derivatives for optimal error estimatesof orthogonal polynomial approximations to functions with limited regularity.It naturally arises from exact representations of orthogonal polynomialexpansion coefficients. Here, the essential pieces of the puzzle for the erroranalysis include (i) fractional integration by parts (under the weakest possibleconditions), and (ii) generalised Gegenbauer functions of fractional degree(GGF-Fs): a new family of special functions with notable fractional calculusproperties.
邀请人：陈升