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Spectral invariance for certain algebras of pseudodifferential operators

Robert Lauter·Bertrand Monthubert·Victor Nistor
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Abstract

We construct algebras of pseudodifferential operators on a continuous family groupoid G that are closed under holomorphic functional calculus, contain the algebra of all pseudodifferential operators of order 0 on G as a dense subalgebra, and reflect the smooth structure of the groupoid G, when G is smooth. As an application, we get a better understanding on the structure of inverses of elliptic pseudodifferential operators on classes of non-compact manifolds. For the construction of these algebras closed under holomorphic functional calculus, we develop three methods: one using two-sided semi-ideals, one using commutators, and one based on Schwartz spaces on the groupoid.

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Robert Lauter, Bertrand Monthubert, Victor Nistor. 2001-12-10. Spectral invariance for certain algebras of pseudodifferential operators. https://arxiv.org/abs/math/0112091

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