Decay bounds of generalized eigenvectors of unbounded Jacobi matrices
by
Jan Janas
Institute of Mathematics Polish Academy of Sciences

Decay bounds on generalized eigenvectors of selfadjoint Jacobi matrices in l²(N) are established. Two cases are considered separately and lead to different results: (i) the case in which the spectral parameter lies in a general gap of the spectrum of the Jacobi matrix and (ii) the case of a lower semibounded Jacobi matrix with values of the spectral parameter below the spectrum. It is demonstrated by examples that both results are sharp. An application to a construction of an unbounded Jacobi matrix with dense point spectrum in a gap will discussed (if time permits).

Date received: June 11, 2008