Mercer定理的推广

A Note on Mercer's Theorem

再生核空间的研究是以Mercer核和Mercer定理为基础。由于Mercer定理只对为Lebesgus测度及X为紧集时成立 ,因此Mercer定理的推广对再生核空间的研究具有重要意义。本文将Mercer定理推广到 μ为Borel测度X为非紧的情形 。

The research of the reproducing kernel spaces is based on Mercer kernel and Mercer' Theorem.For Mercer' theorem is only right when μ is a Lebesgue measure.and when X is compact,in this paper we extended the result of Mercer' theorem to the situation that μ is a Borel measure and X is not compact.