Meromorphic continuation of the spectral shift function

Bruneau, Vincent; Petkov, Vesselin

Duke Math. J., Tome 120 (2003) no. 3, p. 389-430 / Harvested from Project Euclid

Résumé

We obtain a representation of the derivative of the spectral shift function $\xi(\lambda,h)$ in the framework of semiclassical "black box" perturbations. Our representation implies a meromorphic continuation of $\xi(\lambda,h)$ involving the semiclassical resonances. Moreover, we obtain a Weyl-type asymptotics of the spectral shift function, as well as a Breit-Wigner approximation in an interval $(\lambda -\delta,\lambda+\delta), 0<\delta<\epsilon h$.

Publié le : 2003-03-15
Classification: 35P25, 47A40, 47A55, 47F05

@article{1085598297,
     author = {Bruneau, Vincent and Petkov, Vesselin},
     title = {Meromorphic continuation of the spectral shift function},
     journal = {Duke Math. J.},
     volume = {120},
     number = {3},
     year = {2003},
     pages = { 389-430},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1085598297}
}

Bruneau, Vincent; Petkov, Vesselin. Meromorphic continuation of the spectral shift function. Duke Math. J., Tome 120 (2003) no. 3, pp.  389-430. http://gdmltest.u-ga.fr/item/1085598297/