Author

Fred Kaul

Publication Date

8-25-2016

Abstract

The decay of the parameters for a Jacobi operator is related to the analyticity of the Jost function associated with J, which is in turn related to the spectral measure of J. Damanik and Simon demonstrated the equivalence between the exponential decay of these parameters and the analyticity of the Jost function on a disk whose radius is given by the rate of decay. In this paper, these equivalences are summarized, and an additional equivalence is shown in the case when the parameters decay super-exponentially. In this case, the Jost function will be an entire function with finite growth order no greater than twice the inverse of the decay rate.

Degree Name

Mathematics

Level of Degree

Masters

Department Name

Mathematics & Statistics

First Advisor

Zinchenko, Maxim

First Committee Member (Chair)

Pereyra, Maria Cristina

Second Committee Member

Skripka, Anna

Language

English

Keywords

spectral theory, jacobi operator, jost function, hilbert space

Document Type

Thesis

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