Department of Mathematics, Box 1917, Brown University, Providence, Rhode Island 02912
Abstract:
Let be a Jacobi matrix with elements on the main diagonal and elements on the auxiliary ones. We suppose that is a compact perturbation of the free Jacobi matrix. In this case the essential spectrum of coincides with , and its discrete spectrum is a union of two sequences , tending to . We denote sequences and by and , respectively.
The main result of the note is the following theorem.
Theorem. Let be a Jacobi matrix described above and be its spectral measure. Then if and only if