Reproducing kernel Hilbert spaces

In this chapter, we establish the fundamental theorems of linear transforms. The theorems will be naturally related to the idea of reproducing kernel Hilbert spaces and therefore we essentially need the properties of the spaces. So, we shall introduce the general properties of reproducing kernel Hilbert spaces which are needed in concrete applications of the fundamental theorems. This chapter will present a unified and self-contained theory for reproducing kernel Hilbert spaces.