Friday, May 25, 2012

1205.5321 (Matthew Bledsoe)

Stability of the inverse resonance problem for Jacobi operators    [PDF]

Matthew Bledsoe
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.
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