DIFFERENCE SCHRODINGER-OPERATORS WITH LINEAR AND EXPONENTIAL DISCRETESPECTRA

Using the factorization method, we construct finite-difference Schrodi nger operators (Jacobi matrices) whose discrete spectra are composed f rom independent arithmetic, or geometric series. Such systems originat e from the periodic, or q-periodic closure of a chain of corresponding Darboux transformations. The Charlier, Krawtchouk, Meixner orthogonal polynomials, their q-analogs, and some other classical polynomials ap pear as the simplest examples for N = 1 and N = 2 (N is the period of closure). A natural generalization involves discrete versions of the P ainleve transcendents.