Document Type

Dissertation

Date of Degree

Summer 2013

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mathematics

First Advisor

Palle Jorgensen

Abstract

By first looking at the orthonormal basis: Γ = {∑i 4 ibi ∈{0, 1}, finite sums} and the related orthonormal basis 5Γ = {5∑i 4i bi : bi ∈ {0, 1}, finite sums} we find several interesting relationships with the unitary matrix Uα,β arising from the operator U: Γ → 5Γ. Further, we investigate the relationships between U and the operators So : Γ → 4Γ defined by Soe where eγ = e2ΠiΓ and S1: Γ → 4Γ+1 defined by S1eγ = e4γ+1.

Most intriguing, we found that when taking powers of the aforementioned Uα,β matrix that although there are infinitely many 1's occurring in the entries of Uα,β only one such 1 occurs in the subsequent higher powers Ukα,β. This means that there are infinitely many γ ∈ Γ ∩ 5Γ, but only one such γ in the intersection Γ and 5kΓ, for k ≥ 2.

Keywords

infinite matrices

Pages

vi, 58 pages

Bibliography

Includes bibliographical references (pages 57-58).

Copyright

Copyright 2013 Corissa Marie Goertzen

Included in

Mathematics Commons

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