The Theory Of Reproducing Kernel In Hilbert Spaces

This is a report about Reproducing kernel on Hilbert Spaces.It consists of three parts.The first part focuses on the regeneration of reproducing kernel, and introduces some definitions needed. The second part is mainly about some representation theorems and results of reproducing kernel when the Hilbert space consists of analytic functions on the unit disk. In part three, we extend the results of part 2 to multi-dimensional case.At last we will give some classification of some types of reproducing kernel Hilbert space by using some geometrical methods in operator theory. This gives a new proof of the classification.