6533b821fe1ef96bd127ae63

RESEARCH PRODUCT

SPECTRAL INVARIANCE FOR CERTAIN ALGEBRAS OF PSEUDODIFFERENTIAL OPERATORS

Victor NistorRobert LauterBertrand Monthubert

subject

Mathematics::Operator AlgebrasPseudodifferential operatorsGeneral Mathematics010102 general mathematicsMathematics - Operator Algebras01 natural sciencesMathematics - Spectral TheoryAlgebraMathematics Subject ClassificationOperator algebraMathematics::K-Theory and Homology0103 physical sciencesFOS: Mathematics010307 mathematical physics0101 mathematicsOperator Algebras (math.OA)Construct (philosophy)Spectral Theory (math.SP)Mathematics::Symplectic GeometryMathematics

description

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.

yearjournalcountryeditionlanguage
2001-12-10Journal of the Institute of Mathematics of Jussieu
https://doi.org/10.1017/s1474748005000125