报告题目：Polynomial Approximation of Singular Functions in New Fractional Spaces

报告时间：2022-11-04  14:00 - 15:00

报告人：刘文杰 副教授  哈尔滨工业大学

腾讯会议ID：725-269-886

Abstract：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.