Examples of discrete operators with a pure point spectrum of finite multiplicity

One constructs operators acting on l(2)(Z(m)) (or l(2)(Z(m))(p)), m, p grea ter than or equal to 1, with a real pure point spectrum of finite multiplic ity by perturbing diagonal matrices using a KAM procedure. The point spectr um can be dense on an interval or a Cantor set of measure zero. The basic f act here is to remark that for perturbations built up with an infinite numb er of block diagonals, regularly separated, it is possible to deal with eig envalues of multiplicity strictly greater than 1. Examples of discrete oper ators associated with discretization of systems of partial differential equ ations are given. (C) 1999 Academic Press.