一类函数空间及其应用

A Class Function Spaces and Their Applications

本文运用缓增分布的 Hermite 表示理论,引进了一类函数空间并初步讨论了它们的基本性质.在此基础上建立了映 S(R^n)到 S′(R^n)的连续线性算子的 Hermite 表示理论.

This paper is a preparation for the study of linear partial differentialoperators on R^n with polynominal coefficients.A class function spaces isintroduced by using the Hermite expansion theory of temperate distributions,and the Hermite expansion theory of various continuous linear maps onS(R^n)and S′(R^n)is studied.