Ab. Demonvel et al., BOUNDARY-VALUES OF RESOLVENT FAMILIES AND PROPAGATION PROPERTIES, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 322(3), 1996, pp. 289-294
Let H be a self-adjoint operator, A an operator locally conjugate to H
on some open real set, and P-+, P_ the spectral projections of A corr
esponding to the intervals [0, infinity) and (-infinity, 0] respective
ly. We study the local regularity properties of the functions lambda -
-> P-+/- (H - lambda +/- i 0)(-1) epsilon B (H-s, H-t), where {H-s}(s
epsilon R) is the Sobolev scale associated to A. As a corollary we obt
ain propagation theorems for the group {e(iHt)}.