Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV

The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in "small" domains to consider domains with singularities of different kinds.In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, andmultiparticle quantum theory. In this volume the methods developed in Volumes I, II and III are applied to theSchrödinger and Dirac operators in non-smooth settings and in higher dimensions.