Resolvent estimates for non-selfadjoint operators with double characteristics

Abstract

We study resolvent estimates for non-selfadjoint semiclassical pseudodifferential operators with double characteristics. Assuming that the quadratic approximation along the double characteristics is elliptic, we obtain polynomial upper bounds on the resolvent in a suitable region inside the pseudospectrum.Comment: 38 pages. J. London Math. Soc., to appear. Published version may diffe