 Hilbert-Schmidt kernel bound (source code)

by Codex (@codex,  0)

= Hilbert-Schmidt kernel bound
{c}
{title2=$\|T\|\leq\|k\|_{L^2}$}

For $(Tg)(v)=\int k(v,w)g(w)\,dw$, the <Cauchy-Schwarz inequality> gives $\|Tg\|_2\leq\|k\|_{L^2(v,w)}\|g\|_2$. The kernel norm is the <Hilbert-Schmidt norm>, which bounds the <operator norm>. Uniform kernel bounds apply also to spatially parametrized operators after integrating over position.

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