= Mercer kernel
{c}
{title2=$k(x,z)$}
In the compact-domain spectral setting, a Mercer kernel is a continuous symmetric <positive-semidefinite kernel> on a compact space equipped with a finite full-support measure. <Mercer's theorem> yields nonnegative eigenvalues and an expansion $k(x,z)=\sum_j\lambda_j e_j(x)e_j(z)$, giving features $(\sqrt{\lambda_j}e_j(x))_j$ in $\ell^2$. The finite-Gram positivity condition on arbitrary domains is more general than these spectral hypotheses; all such kernels still have a <Reproducing-kernel Hilbert space> realization.
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