S. Denisov, S. Kupin.
On the singular spectrum of Schrodinger 
operators with decaying potentials.
(43K, LATEX)

ABSTRACT.  The relation between Hausdorff dimension of the singular spectrum 
of a Schrodinger operator and the decay of its potential has been 
extensively studied. In this work, we address similar questions 
from a different point of view. Our approach relies on the study of 
the so-called Krein systems. For Schrodinger operators, we show that 
some bounds on the singular spectrum, obtained recently by Remling, 
are optimal in L^p (R^+) scale.