论文标题
连续功能家族的必要条件，形成Karhunen-Loève的基础
Necessary and sufficient conditions for a family of continuous functions to form a Karhunen-Loève basis
论文作者
论文摘要
给定连续函数$（f_ {n}）_ {n} $一致的$ l^{2}（d）$的正顺式系统，带有$ d \ subset \ subset \ mathbb {r}^{d}^{d} $ compact，并给定严格的积极系数$（λ______________当且仅当部分总和$ \ sum_ {j \ leq n}λ_{J} f _ {J} f_ {J}^{2} $等于等于$ d $的情况下。
Given an orthonormal system of $L^{2}(D)$ consistent of continuous functions $(f_{n})_{n}$, with $D \subset \mathbb{R}^{d}$ compact, and given a sequence of strictly positive coefficients $(λ_{n})_{n}$ forming a convergent series, we prove that they consist in the eigenfunctions and eigenvectors of a covariance operator associated to a continuous positive-definite Kernel if and only if the sequence of partial sums $ \sum_{j \leq n} λ_{j} f_{j}^{2} $ is equicontinuous over $D$.
