Finite Gap Jacobi Matrices: An Announcement
Jacob S. Christiansen, Barry Simon, and Maxim Zinchenko
TL;DR
This paper discusses Jacobi matrices with finite gap spectra, focusing on Szego's theorem, Jost solutions, and asymptotics, providing insights into their spectral properties and asymptotic behaviors.
Contribution
It introduces new results on Szego's theorem and asymptotics for finite gap Jacobi matrices, extending classical spectral theory to this setting.
Findings
Analysis of Szego's theorem in finite gap context
Development of Jost solutions for these matrices
Asymptotic descriptions of spectral measures
Abstract
We consider Jacobi matrices whose essential spectrum is a finite union of closed intervals. We focus on Szego's theorem, Jost solutions, and Szego asymptotics for this situation. This announcement describes talks the authors gave at OPSFA 2007.
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