We consider an arbitrary linear elliptic firstorder 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 AU 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 wellposed selfadjoint Fredholm extensions under continuous variation of the data.
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@book{98401b20feeb11dca1c1000ea68e967b,
title = "The Calderon Projection: New Definition and Applications",
abstract = "We consider an arbitrary linear elliptic firstorder 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 AU 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 wellposed selfadjoint Fredholm extensions under continuous variation of the data.",
author = "Bernhelm BoossBavnbek and Matthias Lesch and Chaofeng Zhu",
year = "2008",
language = "English",
publisher = "ArXiv.org  Cornell University",
address = "United States",
}
TY  RPRT
T1  The Calderon Projection
T2  New Definition and Applications
AU  BoossBavnbek, Bernhelm
AU  Lesch, Matthias
AU  Zhu, Chaofeng
PY  2008
Y1  2008
N2  We consider an arbitrary linear elliptic firstorder 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 AU 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 wellposed selfadjoint Fredholm extensions under continuous variation of the data.
AB  We consider an arbitrary linear elliptic firstorder 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 AU 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 wellposed selfadjoint Fredholm extensions under continuous variation of the data.
M3  Report
BT  The Calderon Projection
PB  ArXiv.org  Cornell University
CY  www.arxiv.org
ER 