The Calderon Projection: New Definition and Applications

Bernhelm Booss-Bavnbek, Matthias Lesch, Chaofeng Zhu

Publikation: Bog/antologi/afhandling/rapportRapportForskning


We consider an arbitrary linear elliptic first--order differential operator A with smooth coefficients acting on sections of a complex vector bundle E over a compact smooth manifold M with smooth boundary. We describe the analytic and topological properties of A in a collar neighborhood U of the boundary 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 self-adjoint Fredholm extensions under continuous variation of the data.
OriginalsprogEngelsk - Cornell University
Antal sider58
StatusUdgivet - 2008

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