THE EMBEDDING THEORY OF NATIVE SPACES
Lin-Tian Luh
【期刊名称】《分析、理论与应用（英文版）》 【年(卷),期】2001(017)004
【摘要】In the theory of radial basis functions,mathematicians use linear combinations of the translates of the radial basis functions as interpolants.The set of these linear combinations is a normed vector space.This space can be completed and become a Hilbert space,called native space,which is of great importance in the last decade.The native space then contains some abstract elements which are not linear combinations of radial basis functions.The meaning of these abstract elements is not fully known.This paper presents some interpretations for the these elements.The native spaces are embedded into some well-known spaces.For example,the Sobolev-space is shown to be a native space.Since many differential equa tions have sdutions in the Sobolev-space ,we can therefore approximate the sdutions by linear combinations of radial basis functions.Moreover,the famous question of the embedding of the native space into L2 (Ω) is also solved by the author.
【总页数】15页(90-104) 【关键词】
【作者】Lin-Tian Luh
THE EMBEDDING THEORY OF NATIVE SPACES
