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Regularity of the integrated density of states in the continuous spectrum

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  • M. Krishna

    (Ashoka University)

Abstract

In this paper we show that spectral measures of the Laplacian on $$\ell ^2({\mathbb {Z}}^d)$$ ℓ 2 ( Z d ) are smooth in some regions of its spectrum, a result that extends to parts of the absolutely continuous spectrum of some random perturbations of it. The spectral measures considered are associated with dense sets of vectors.

Suggested Citation

  • M. Krishna, 2024. "Regularity of the integrated density of states in the continuous spectrum," Indian Journal of Pure and Applied Mathematics, Springer, vol. 55(3), pages 957-965, September.
    • Handle: RePEc:spr:indpam:v:55:y:2024:i:3:d:10.1007_s13226-024-00640-1
    DOI: 10.1007/s13226-024-00640-1
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