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.
Level of Degree
Mathematics & Statistics
First Committee Member (Chair)
Pereyra, Maria Cristina
Second Committee Member
spectral theory, jacobi operator, jost function, hilbert space
Kaul, Fred. "Jost Functions for Jacobi Operators with Super-exponentially Decaying Parameters." (2016). https://digitalrepository.unm.edu/math_etds/23