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A Hilbert space $H$ is a real or complex vector space endowed with an inner product such that $H$ is a complete metric space when endowed with the norm induced by this inner product.

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RKHS norm of Lipschitz functions

I think that in general $L(.)$ and $\Vert.\Vert_\mathcal{H}$ measure quite different things. Writing $L(f)$ for $$ \inf\{ M>0:|f(x)-f(x')| \leq Md(x,y) \;\forall \;x,x'\in \mathcal{X}\} $$ let $\mathc …
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