Complete Differentiable Semiclassical Spectral Asymptotics

Abstract

For an operator $A:=A_h=A^0(hD)+V(x,hD)$ with a "potential" $V$ decaying as $|x|\to \infty$ we establish under certain assumptions the complete and differentiable with respect to $\tau$ asymptotics of $e_h(x,x,\tau )$ where $e_h(x,y,\tau )$ is the Schwartz kernel of the spectral projector.

12pp