 Reproducing kernel Hilbert space

A reproducing-kernel Hilbert space is a Hilbert space of functions in which point evaluation is continuous and satisfies $f(x)=⟨f,k(x,\cdot )⟩$.

A Reproducing Kernel Hilbert Space (RKHS) is a fundamental concept in functional analysis and machine learning, particularly in the context of kernel methods. It is a Hilbert space of functions in which point evaluations are continuous linear functionals. The main feature of an RKHS is the presence of a reproducing kernel, which allows for an elegant and powerful way to characterize functions in the space.