ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 47, 81 Geyler, Vladimir, Mordovian State University, Saransk, Russia Periodic point interactions on a Riemannian manifold Let X be a complete n-dimensional Riemannian manifold on which a group Γ acts isometrically, effectively, and properly discontinuously with compact Γ \ X. For a Γ-periodic, self-adjoint elliptic operator A_{0} of order m > n/2 in L^{2}(X), we consider a Γ-periodic point perturbation A of A_{0}. It is proved that the gaps of the spectrum σ(A) are labelled in a natural way by elements of the K_{0}-group of a certain C^{∗}-algebra. In particular, if this algebra has the Kadison property, then σ(A) has band structure. Part of these results is obtained jointly with J. Brüning.