0000000000421943

AUTHOR

Bertrand Monthubert

showing 2 related works from this author

Invariance spectrale des algèbres d'opérateurs pseudodifférentiels

2002

We construct and study several algebras of pseudodifferential operators that are closed under holomorphic functional calculus. This leads to a better understanding of the structure of inverses of elliptic pseudodifferential operators on certain non-compact manifolds. It also leads to decay properties for the solutions of these operators. To cite this article: R. Lauter et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 1095–1099.

AlgebraOperator algebraBanach algebraFredholm operatorHolomorphic functional calculusHolomorphic functionGeneral MedicineOperator theoryFréchet algebraDifferential operatorMathematicsComptes Rendus Mathematique
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SPECTRAL INVARIANCE FOR CERTAIN ALGEBRAS OF PSEUDODIFFERENTIAL OPERATORS

2001

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.

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 GeometryMathematicsJournal of the Institute of Mathematics of Jussieu
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