BOUNDARY-VALUES OF RESOLVENT FAMILIES AND PROPAGATION PROPERTIES

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)}.