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 Committee Member (Chair)
Maxim Zinchenko
Second Committee Member
Anna Skripka
Third Committee Member
Maria Cristina Pereyra
Language
English
Keywords
spectral theory, jacobi operator, jost function, hilbert space
Document Type
Thesis
Recommended Citation
Kaul, Fred II. "Jost Functions for Jacobi Operators with Super-exponentially Decaying Parameters." (2016). https://digitalrepository.unm.edu/math_etds/23
