Analysis of Five Diagonal Reproducing Kernels

The focus of this work is on a specific class of reproducing kernel Hilbert spaces. In Adams and McGuire [2], the tridiagonal reproducing kernels were introduced, and in [3], a specific example of a tridiagonal reproducing kernel Hilbert space was investigated. In particular, a careful functional comparison was made between this tridiagonal space and the well-known Hardy space. This tridiagonal example is studied further in this thesis via the determination of the spectrum of the multiplication by z operator. The main results of this thesis generalize this example to the five diagonal case. A general framework is developed for functionally comparing different bandwidth spaces, and this framework is applied to outline the relationship between the generalized five diagonal example and the Hardy space