942 research outputs found
The Calderon Projection: New Definition and Applications
We consider an arbitrary linear elliptic first--order differential operator A
with smooth coefficients acting between sections of complex vector bundles E,F
over a compact smooth manifold M with smooth boundary N. We describe the
analytic and topological properties of A in a collar neighborhood U of N and
analyze various ways of writing A|U in product form. We discuss the sectorial
projections of the corresponding tangential operator, construct various
invertible doubles of A by suitable local boundary conditions, obtain Poisson
type operators with different mapping properties, and provide a canonical
construction of the Calderon projection. We apply our construction to
generalize the Cobordism Theorem and to determine sufficient conditions for
continuous variation of the Calderon projection and of well--posed selfadjoint
Fredholm extensions under continuous variation of the data.Comment: 60 pages, 4 figures; revised version; index and list of notation
added; accepted for publication in J. Geom. Phys; v3 contains a few minor
correction
Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds I: Resolvent construction at high energy
This is the first in a series of papers in which we investigate the resolvent
and spectral measure on non-trapping asymptotically hyperbolic manifolds with
applications to the restriction theorem, spectral multiplier results and
Strichartz estimates. In this first paper, we use semiclassical Lagrangian
distributions and semiclassical intersecting Lagrangian distributions, along
with Mazzeo-Melrose 0-calculus, to construct the high energy resolvent on
general non- trapping asymptotically hyperbolic manifolds, generalizing the
work due to Melrose, Sa Barreto and Vasy. We note that there is an independent
work by Y. Wang which also constructs the high-energy resolvent.Comment: 49 page
- …