%0 Journal Article
%T Spectral shift function for slowly varying perturbation of periodic Schr£¿dinger operators
%A Dimassi
%A Mouez
%A Zerzeri
%A Maher
%J Cubo (Temuco)
%D 2012
%I Scientific Electronic Library Online
%R 10.4067/S0719-06462012000100004
%X in this paper we study the asymptotic expansion of the spectral shift function for the slowly varying perturbations of periodic schr£¿dinger operators. we give a weak and pointwise asymptotic expansions in powers of h of the derivative of the spectral shift function corresponding to the pair(p(h) = p0 + ¦Õ (hx); p0 = -¦Ä+ v(x)) ; where is a decreasing function, o (|x|-¦Ä) for some ¦Ä> n and h is a small positive parameter. here the potential v is real, smooth and periodic with respect to a lattice t in rn. to prove the pointwise asymptotic expansion of the spectral shift function, we establish a limiting absorption theorem for p(h).
%K periodic schr£¿dinger operator
%K spectral shift function
%K asymptotic expansions
%K limiting absorption theorem.
%U http://www.scielo.cl/scielo.php?script=sci_abstract&pid=S0719-06462012000100004&lng=en&nrm=iso&tlng=en