%0 Journal Article %T Finite Gap Jacobi Matrices: An Announcement %A Jacob S. Christiansen %A Barry Simon %A Maxim Zinchenko %J Mathematics %D 2007 %I arXiv %X 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. %U http://arxiv.org/abs/0711.4739v1