Reproducing Kernel Hilbert Spaces (RKHS) are a special type of Hilbert space that allow for the evaluation of functions at specific points using inner products. They are characterized by a reproducing kernel, which is a positive definite function that enables the representation of evaluation functionals as inner products. This property makes RKHS particularly useful in machine learning and statistics. In RKHS, each point in the input space corresponds to a unique function in the space, facilitating the analysis of complex data. The concept is closely related to Mercer’s theorem, which provides conditions under which a kernel can be represented as an inner product in a Hilbert space.