紧致齐性空间上的调和分析(Ⅰ)——富里埃级数的Poisson求和

Harmonic Analysis on Compact Homogeneous Spaces (Ⅰ)

首先介绍了紧致齐性空间上调和分析的若干基础性结果,并给出这些结果的较简洁的证明。接着,我们定义了紧致齐性空间上函数的卷积(熟知n维球面是一个紧致齐性空间),这一定义看来对研究紧致齐性空间上的调和分析向题是相当有用的。最后,用定义的卷积,研究了紧致齐性空间上Fourier级数的Poisson求和。

In this paper, some basic results of harmonic analysis on compact homogeneous spaces are introduced, and some simple proofs for these known results are also given in the first part of this paper.Then a definition of convolution of functions on the spaces is given. (It is known that n-dimentional sphere is a compact homogeneous space.) It seems that the definition of convolution is useful for studying various subjects of harmonic analysis on these spaces.By using the definition of convolution, Poisson summability of Fourier series on the spaces is discussed.