Reproducing kernel

In functional analysis (a branch of mathematics), a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional. Roughly speaking, this means that if two functions ${\displaystyle f}$ and ${\displaystyle g}$ in the RKHS are close in norm, i.e., ${\displaystyle \|f-g\|}$ is small, then ${\displaystyle f}$ and ${\displaystyle g}$ are also pointwise close, i.e., ${\displaystyle |f(x)-g(x)|}$ is small for all ${\displaystyle x}$. The reverse need not be true.

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