Unbounded Jacobi Matrices with a Few Gaps in the Essential Spectrum: Constructive Examples

Abstract

We give explicit examples of unbounded Jacobi operators with a few gaps in their essential spectrum. More precisely a class of Jacobi matrices whose absolutely continuous spectrum fills any finite number of bounded intervals is considered. Their point spectrum accumulates to +∞ and -∞. The asymptotics of large eigenvalues is also found. © 2010 The Author(s).