报告题目：Polynomial approximation of singular functions in new fractional spaces

报 告 人：刘文杰副教授（哈尔滨工业大学）

报告时间：2022年9月28日  15:30

报告地点：腾讯会议（231657697）

报告摘要：

In this talk, we introduce a new theoretical framework built upon fractional spaces 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)，(ii) fractional taylor formula, (iii) generalised Gegenbauer functions of fractional degree (GGF-Fs): a new family of special functions with notable fractional calculus properties, and (iv) asymptotic formulas or uniform upper bounds of GGF-Fs. Finally we introduce the hypothesis of Babuska and Hakula.

报告人简介：

刘文杰，现为哈尔滨工业大学数学学院副教授。曾经为新加坡南洋理工大学的Research Fellow。主要研究谱方法及其应用、多项式逼近理论、具奇异问题的hp有限元法等。获得中国博士后科学基金面上项目、国家自然科学基金青年项目和面上项目的资助。在Mathematics of Computation、Journal of Approximation Theory、Journal of Computational Physics等国际著名期刊发表SCI论文19篇。