Date of Thesis


Thesis Type

Honors Thesis

Degree Type

Bachelor of Science



First Advisor

Gregory T. Adams

Second Advisor

Paul J. McGuire


Hilbert space, Reproducing kernel, Finite bandwidth, Five diagonal


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.