Mathematics – Differential Geometry
Scientific paper
2008-03-28
Journal of Geometry and Physics 59, No 7, (2009), 784-826
Mathematics
Differential Geometry
60 pages, 4 figures; revised version; index and list of notation added; accepted for publication in J. Geom. Phys; v3 contains
Scientific paper
10.1016/j.geomphys.2009.03.012
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.
Booss-Bavnbek Bernhelm
Lesch Matthias
Zhu Chaofeng
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