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.
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Brüning, J., Geyler, V.A. (2000). The Spectrum of Periodic Point Perturbations and the Krein Resolvent Formula. In: Adamyan, V.M., et al. Differential Operators and Related Topics. Operator Theory: Advances and Applications, vol 117. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8403-7_7
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DOI: https://doi.org/10.1007/978-3-0348-8403-7_7
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