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Absolute continuity of the spectrum of the periodic Schrödinger operator in a layer and in a smooth cylinder

The Schrödinger operator H = −Δ + V is considered in a layer or in a d-dimensional cylinder. The potential V is assumed to be periodic with respect to a lattice. The absolute continuity of H is established, provided that VL p,loc, where p is a real number greater than d/2 in the case of a layer and p > max(d/2, d − 2) for a cylinder. Bibliography: 14 titles.

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Correspondence to I. Kachkovskiy.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 385, 2010, pp. 69–82.

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Kachkovskiy, I., Filonov, N. Absolute continuity of the spectrum of the periodic Schrödinger operator in a layer and in a smooth cylinder. J Math Sci 178, 274 (2011). https://doi.org/10.1007/s10958-011-0547-8

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Keywords

  • Russia
  • Real Number
  • Potential Versus
  • Mathematical Institute
  • Spectral Cluster