Uniqueness of multiplicative determinants on elliptic pseudodifferential operators
Résumé
We describe all multiplicative determinants on the pathwise connected component of identity in the group of invertible classical pseudodifferential operators on a closed manifold, that are continuous along continuous paths and the restriction to zero order operators of which is of class C 1. This boils down to a description of all traces on zero order classical pseudodifferential operators, which turn out to be linear combinations of the Wodzicki residue [W] and leading symbol traces introduced in [PR1], both of which are continuous. Consequently, multi-plicative determinants are parametrized by the residue determinant [W87, Sc] and a new "leading symbol determinant", both of which are expressed in terms of a homogeneous component of the symbol of the logarithm of the operator.
Domaines
Algèbres d'opérateurs [math.OA]Origine | Fichiers produits par l'(les) auteur(s) |
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