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Fredholm realizations of elliptic symbols on manifolds with boundary
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Pierre Albin
Published/Copyright:
January 8, 2009
Abstract
We show that the existence of a Fredholm element of the zero calculus of pseudodifferential operators on a compact manifold with boundary with a given elliptic symbol is determined, up to stability, by the vanishing of the Atiyah-Bott obstruction. It follows that, up to small deformations and stability, the same symbols have Fredholm realizations in the zero calculus, in the scattering calculus, and in the transmission calculus of Boutet de Monvel.
Received: 2007-04-26
Revised: 2007-11-03
Published Online: 2009-01-08
Published in Print: 2009-February
© Walter de Gruyter Berlin · New York 2009
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Articles in the same Issue
- Entire spacelike hypersurfaces of constant Gauß curvature in Minkowski space
- On the growth of nonuniform lattices in pinched negatively curved manifolds
- Extended Picard complexes and linear algebraic groups
- Birationality of étale maps via surgery
- Heights and metrics with logarithmic singularities
- Fredholm realizations of elliptic symbols on manifolds with boundary
- Correspondences with split polynomial equations
- A parabolic free boundary problem with Bernoulli type condition on the free boundary
