Project Director

Nichols, Roger

Department Examiner

Barioli, Francesco; Cox, Christopher L. (Christopher Lee)

Department

Dept. of Mathematics

Publisher

University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)

Abstract

In this project, we investigate positive definite sequences and their associated Jacobi matrices in Hilbert space. We set out to determine the Jacobi matrix associated to the Hilbert sequence by methods described in Akhiezer’s book The Classical Moment Problem. Using methods in Teschl’s book Jacobi Operators and Completely Integrable Nonlinear Lattice, we determine the essential spectrum of the corresponding Jacobi matrix.

Acknowledgments

My thanks to the University of Tennessee at Chattanooga’s Department of Mathematics and Honors College for allowing me to do this project. Thank you Dr. Roger Nichols who guided me on this project.

Degree

B. A.; An honors thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Bachelor of Arts.

Date

5-2023

Subject

Jacobi operators; Functional analysis

Keyword

Hilbert Sequence; Jacobi Matrices; Hilbert Space

Discipline

Algebra

Document Type

Theses

Extent

v, 20 leaves

DCMI Type

Text

Language

English

Rights

http://rightsstatements.org/vocab/InC/1.0/

License

http://creativecommons.org/licenses/by/4.0/

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Included in

Algebra Commons

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