where x(z) = ∑∞ j=1 xjz j is the symbol of the operator. In terms of the Hardy polarization of odd spinors on S, B1(x) = P+MxP−, where P+, P− are projections and Mx is the multiplication operator corresponding to x. The map x 7−→ B1(x) is conformally equivariant in a sense explained in §2. In this paper we derive explicit expressions for certain well-known higher-order generalizations of this m...

We study the index theory of a class perturbed Dirac operators on non-compact manifolds form D+ic(X), where c(X) is Clifford multiplication operator by an orbital vector field with respect to action compact Lie group. Our main result that such factors as KK-product certain KK-theory classes defined D and X. As corollary we obtain excision cobordism-invariance properties first established Braver...

We define the decomposition property for partial actions of discrete groups on C⁎-algebras. Decomposable systems appear naturally in practice, and many commonly occurring can be decomposed into with property. For instance, any action a finite group is an iterated extension decomposable systems. Partial are always globalizable amenable, regardless acting group, their globalization explicitly des...