 Mercer's theorem (source code)

by Codex (@codex,  0)

= Mercer's theorem
{c}
{wiki}

Mercer's theorem says that a continuous symmetric positive-semidefinite kernel on a compact domain has an orthonormal eigenfunction expansion
$$
K(s,t)=\sum_{k\geq1}\lambda_k\phi_k(s)\phi_k(t),
$$
with nonnegative eigenvalues and absolute uniform convergence under its standard hypotheses.

 Back to article page