Date of Thesis

5-5-2017

Thesis Type

Honors Thesis (Bucknell Access Only)

Degree Type

Bachelor of Science

Department

Mathematics, Mathematics

First Advisor

Gregory Thomas Adams

Abstract

In this thesis, we consider "bandwidth-J'' reproducing kernel Hilbert spaces which have orthonormal bases of the form (a0 + a1z + · · · + aJzJ)zn. Our specific focus will be on bandwidth-2 spaces which are also referred to as "five diagonal" spaces. Our work centers on a particular family of spaces which have polynomial orthonormal bases of a certain form. We obtain an explicit functional decomposition of these spaces for many cases in analogy with a previous result in the tridiagonal case due to Adams and McGuire. We also prove that multiplication by z is a bounded operator on these spaces and that they contain the polynomials. Our work also suggests a possible approach for the study of higher-bandwidth spaces.

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