Reproducing kernel Hilbert space

In functional analysis, a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional. Specifically, a Hilbert space H {\displaystyle H} of functions from a set X {\displaystyle X} (to R {\displaystyle \mathbb {R} } or C {\displaystyle \mathbb {C} } ) is an RKHS if the point-evaluation functional L x : H → C {\displaystyle L_{x}:H\to \mathbb {C} } , L x ( f ) = f ( x ) {\displaystyle L_{x}(f)=f(x)} , is continuous for every x ∈ X {\displaystyle x\in X} .

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