A.Laptev, S.Naboko, O.Safronov
On new relations between spectral 
properties of Jacobi matrices and their coefficients
(195K, Postscript)

ABSTRACT.  We study the spectral properties of Jacobi 
matrices. 
By using "higher order" trace formulae we obtain 
a result relating the properties of the elements 
of Jacobi matrices and the corresponding spectral measures. 
Complicated expressions for traces of some 
operators can be magically simplified allowing us to apply 
induction arguments. Our theorems are generalizations 
of a recent result of R. Killip and B. Simon.