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.

Addeddate 2013-09-18 21:28:05 External-identifier urn:arXiv:0803.4160 Identifier arxiv-0803.4160 Identifier-ark ark:/13960/t87h44663 Ocr ABBYY FineReader 9.0 Ppi 300 Scanner Internet Archive Python library 0.3.2 Source http://arxiv.org/abs/0803.4160v3

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