Discrete spectra criteria for certain classes of singular differential anddifference operators

In this paper, we consider singular differential and difference operators o f the form m(y) equivalent to (-1)(n)/omega (t) (r(t)y((n)))((n)) and b(y)(k+n) equiva lent to (-1)(n)/omega (k) Delta (n)(r(k)Delta (n)y(k)), as well as their full-term analogies. We establish criteria for discretenes s and boundedness below of their spectrum-property ED. Difference operators are studied as the discrete counterparts of the continuous ones. (C) 2001 Elsevier Science Ltd. All rights reserved.