Amour L., Guillot J. -C.
Examples of discrete operators with a pure point spectrum of finite
multiplicity.
(30K, Latex)
ABSTRACT. One constructs
operators acting on $\l^2(\Z^m)$
(or $\l^2(\Z^m)^p$), $m,p\geq 1$, with a real pure point spectrum
of finite multiplicity by perturbing diagonal matrices using
a KAM procedure. The point spectrum can be dense on an interval
or a Cantor set of measure zero. The basic fact here is to
remark that for perturbations built up with an infinite number
of block diagonals, regularly separated, it is possible to deal with
eigenvalues of multiplicity strictly greater than one. Examples of
discrete operators associated with discretization of systems of partial
differential equations are given.