The space of such functions is known as a reproducing kernel Hilbert space.

Reproducing kernel Hilbert space Mapping the points to a higher dimensional feature space

http://www.gatsby.ucl.ac.uk/~gretton/coursefiles/lecture4_introToRKHS.pdf

【We next show that every reproducing kernel Hilbert space has a unique positive definite kernel, and vice-versa: this is the Moore-Aronszajn theorem.】

每个可繁殖核希尔伯特空间有一个唯一的正定的核。

Every positive definite kernel k is associated with a unique RKHS H.

We have introduced the notation of feature spaces, and kernels on these feature spaces. What’s more, we’ve determined that these kernels are positive definite. In this section, we use these kernels to define functions on X . The space of such functions is known as a reproducing kernel Hilbert space.

【函数空间-RKHS】