The Calderon Projection: New Definition and Applications

Abstract

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.

60 pages, 4 figures; revised version; index and list of notation added; accepted for publication in J. Geom. Phys; v3 contains a few minor corrections

References in corpus (3)

• The invertible double of elliptic operators
• General Spectral Flow Formula for Fixed Maximal Domain
• Weak Symplectic Functional Analysis and General Spectral Flow Formula

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