摘要：

In this talk, we introduce a new theoretical framework built upon fractional Sobolev-type spaces involving Riemann-Liouville fractional integrals/derivatives for optimal error estimates of orthogonal polynomial approximations to functions with limited regularity. It naturally arises from exact representations of orthogonal polynomial expansion coefficients. Here, the essential pieces of the puzzle for the error analysis include (i) fractional integration by parts (under the weakest possible conditions), and (ii) generalised Gegenbauer functions of fractional degree (GGF-Fs): a new family of special functions with notable fractional calculus properties. (based on joint works with Li-Lian Wang, Huiyuan Li and Boying, Wu)

报告人：

刘文杰博士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及其应用、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。

时间：2020年10月20日周二上午10:00-11:00

地点：腾讯会议 ID：199 657 780

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数学科学学院

2020年10月18日