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The Spectrum of Periodic Point Perturbations and the Krein Resolvent Formula

  • J. Brüning
  • V. A. Geyler
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 117)

Abstract

We study periodic point perturbations H of a periodic elliptic operator H 0 on a connected complete non-compact Riemannian manifold X,endowed with an isometric, effective, properly discontinuous, and co-compact action of a discrete group Γ. Under some conditions H 0, we prove that the gaps of the spectrum σ (H) are labelled in a natural way by elements of the K 0-group of a certain C*-algebra. In particular, if the group Γ has the Kadison property then σ (H) has band structure. The Krein resolvent formula plays a crucial role in proving the main results.

AMS Classification

58625 81Q10 

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Copyright information

© Springer Basel AG 2000

Authors and Affiliations

  • J. Brüning
    • 1
  • V. A. Geyler
    • 2
  1. 1.Institute of MathematicsHumboldt University at BerlinBerlinGermany
  2. 2.Department of MathematicsMordovian State UniversitySaranskRussia

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