The orthogonal polynomial approximation in the reproducing kernel Hilbert space
数学专题报告
报告题目(Title)：The orthogonal polynomial approximation in the reproducing kernel Hilbert space
报告人(Speaker)：张鹤（北京大学）
地点(Place)：腾讯会议：804-262-174
时间(Time)：2022年6月24日15:00-16:00
邀请人(Inviter)：蒋国盛
报告摘要
The reproducing kernel Hilbert space (RKHS) is a particular class of Hilbert space satisfying the reproducing property such that all its elements yield similar properties to the corresponding kernel, e.g., regularity and decay rate. My talk will explore the orthogonal polynomial approximation using an RKHS setup, including
1. construct kernels and RKHS via orthogonal polynomials,
2. discuss the universality (denseness in usual function
spaces) of the resulting RKHS
3. study the approximation error.
My talk will briefly introduce the RKHS theory and show an
application example in density estimation.
