Jost Functions and Jost Solutions for Jacobi Matrices, II. Decay and Analyticity

TL;DR

This paper establishes precise conditions on the Jost function that determine the exponential decay rate of Jacobi matrix parameters, enhancing understanding of their spectral properties.

Contribution

It provides necessary and sufficient conditions linking the Jost function's properties to the decay behavior of Jacobi matrix parameters.

Findings

Conditions for exponential decay of Jacobi parameters

Characterization of Jost functions with decay properties

Implications for spectral analysis of Jacobi matrices

Abstract

We present necessary and sufficient conditions on the Jost function for the corresponding Jacobi parameters $a_n -1$ and $b_n$ to have a given degree of exponential decay.