  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 $(\lambda_{n})_{n}$ 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} \lambda_{j} f_{j}^{2} $
is equicontinuous over $D$.
