An index theorem for Wiener-Hopf operators |
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Authors: | Alexander Alldridge |
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Affiliation: | Institut für Mathematik, Universität Paderborn, Warburger Straße, 33098 Paderborn, Germany |
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Abstract: | We study the multivariate generalisation of the classical Wiener-Hopf algebra, which is the C∗-algebra generated by the Wiener-Hopf operators, given by convolutions restricted to convex cones. By the work of Muhly and Renault, this C∗-algebra is known to be isomorphic to the reduced C∗-algebra of a certain restricted action groupoid. It admits a composition series, and therefore, a ‘symbol’ calculus. Using groupoid methods, we obtain, in the framework of Kasparov's bivariant KK-theory, a topological expression of the index maps associated to these symbol maps in terms of geometric-topological data of the underlying convex cone. This generalises an index theorem by Upmeier concerning Wiener-Hopf operators on symmetric cones. Our result covers a wide class of cones containing polyhedral and homogeneous cones. |
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Keywords: | 47B35 19K56 |
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