Fredholm Realizations of Elliptic Symbols on Manifolds with Boundary Pierre Albin and Richard Melrose
نویسنده
چکیده
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.
منابع مشابه
Fredholm realizations of elliptic symbols on manifolds with boundary II: fibered boundary Citation Albin, Pierre and Richard Melrose. "Fredholm realizations of elliptic symbols on manifolds with boundary II: fibered boundary." in Motives, quantum field theory, and pseudodifferential operators
We consider two calculi of pseudodifferential operators on manifolds with fibered boundary: Mazzeo’s edge calculus, which has as local model the operators associated to products of closed manifolds with asymptotically hyperbolic spaces, and the φ calculus of Mazzeo and the second author, which is similarly modeled on products of closed manifolds with asymptotically Euclidean spaces. We construc...
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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...
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one can quantize an invertible symbol σ ∈ C∞(S∗X; hom(π∗E, π∗F )) as an elliptic pseudodifferential operator in the Φ-b or edge calculus, ΨΦ-b(X;E,F ), introduced in [7] or alternately as an elliptic operator in the Φ-c or φ calculus, ΨΦ-c(X;E,F ), introduced in [8]. As on a closed manifold, either of these operators will induce a bounded operator acting between natural L-spaces of sections but...
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