Microlocal Analysis, Sharp Spectral Asymptotics and Applications III

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, and multiparticle quantum theory.

In this volume the methods developed in Volumes I and II are applied to the Schrödinger and Dirac operators in smooth settings in dimensions 2 and 3.

Research monograph for researchers and graduate students in Mathematics and Mathematical Physics Most comprehensive work about the topic Use of technique, developed by the author during more than 40 years

Auteur

VICTOR IVRII is a professor of mathematics at the University of Toronto. His areas of specialization are analysis, microlocal analysis, spectral theory, partial differential equations and applications to mathematical physics. He proved the Weyl conjecture in 1979, and together with Israel M. Sigal he justified the Scott correction term for heavy atoms and molecules in 1992. He is a Fellow of the Royal Society of Canada (since 1998) and of American Mathematical Society (since 2012).

Contenu
Smooth theory in dimensions 2 and 3.- Standard Theory.- 2D degenerating magnetic Schrödinger operator.- 2D magnetic Schrödinger near boundary.- Magnetic Schrödinger operator: short loops.- Dirac operator with strong magnetic field.