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

被引：0
作者：
Kachkovskiy I. [1 ]
Filonov N. [1 ]
机构：
[1] St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg
来源：
Journal of Mathematical Sciences | 2011年 / 178卷 / 3期
关键词：
Russia; Real Number; Potential Versus; Mathematical Institute; Spectral Cluster;
D O I：
10.1007/s10958-011-0547-8
中图分类号：
学科分类号：
摘要：
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 V ∈ Lp,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. © 2011 Springer Science+Business Media, Inc.
引用
收藏
页码：274 / 281
页数：7
相关论文
共 14 条
  • [1] Birman M., Suslina T.A., Absolute continuity of a two-dimensional periodic magnetic Hamiltonian with discontinuous vector potential, Algebra Analiz, 10, 4, pp. 1-36, (1998)
  • [2] Birman M., Suslina T.A., Periodic magnetic Hamiltonian with variable metrics Problem of absolute continuity, Algebra Aualiz, 11, 2, pp. 1-40, (1999)
  • [3] Danilov L.I., On absolute continuity of the spectrum of a periodic magnetic Schrödinger operator, J. Phys. A: Math. Theor., 42, (2009)
  • [4] Filonov N., Kachkovskii I., Absolute continuity of the spectrum of a periodic Schrödinger operator in a miiltidimensional cylinder, Algebra Analiz, 21, 1, pp. 133-152, (2009)
  • [5] Kato T., Perturbation Theory for Linear Operators, Grundlehren Der Mathematischen Wissenschaften, 132, (1966)
  • [6] Reed M., Simon B., Methods of Modern Mathematical Physics: Analysis of Operators, 4, (1978)
  • [7] Shargorodsky E., Sobolev A.V., Quasiconformal mappings and periodic spectral problems in dimension two, J. Anal. Math., 91, pp. 67-103, (2003)
  • [8] Shen Z., On absolute continuity of the periodic Schrödinger operators, Intern. Math. Res. Notes, 1, pp. 1-31, (2001)
  • [9] Shterenberg R.G., Suslina T.A., Absolute continuity of the spectrum of the Schrödinger operator with the potential concentrated on a periodic system of hypersurfaces, Algebra Analiz, 13, 5, pp. 197-240, (2001)
  • [10] Shterenberg R.G., Suslina T.A., Absolute continuity of the spectrum of the magnetic Schrödinger operator with a metric in a two-dimensional periodic waveguide, Algebra Analiz, 14, 2, pp. 159-206, (2002)
12