2012/05/24 by Matthew Bledsoe, Bledsoe, Matthew
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1205.5321
arxiv created 2012/05/24 · openalex publication_date 2012/05/24 · arxiv updated 2012/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When the coefficients of a Jacobi operator are finitely supported perturbations of the 1 and 0 sequences, respectively, the left reflection coefficient is a rational function whose poles inside, respectively outside, the unit disk correspond to eigenvalues and resonances. By including the zeros of the reflection coefficient, we have a set of data that determines the Jacobi coefficients up to a translation as long as there is at most one half-bound state. We prove that the coefficients of two Jacobi operators are pointwise close assuming that the zeros and poles of their left reflection coefficients are \eps-close in some disk centered at the origin.