arXiv math/06071542006-07math.DGmath.KT

Fredholm realizations of elliptic symbols on manifolds with boundary

Pierre Albin, Richard Melrose

发表信息：: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2009, Issue 627, Pages 155-181

英文摘要：

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.

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