Sergey Naboko: Decay bounds on eigenfunctions and the singular spectrum of unbounded Jacobi matrices

Bounds on the exponential decay of generalized eigenfunctions of bounded and unbounded Jacobi matrices are established.Two cases are considered separately and lead to different results: the case of a bounded gap in the spectrum and the case of semibounded Jacobi matrices.The examples demonstrate the sharpness of the results.
Application of the results  allows to obtain the constructive examples of unbounded Jacobi matrices with a spectral mobility edges, i.e. a transition from purely absolutely continuous spectrum to dense point spectrum.Talk is based on joint work with J.Janas and G.Stolz.