Unbounded Jacobi Matrices with a Few Gaps in the Essential Spectrum: Constructive Examples

被引：0
作者：
Anne Boutet de Monvel
Jan Janas
Serguei Naboko
机构：
[1] Université Paris Diderot Paris 7,Institut de Mathématiques de Jussieu
[2] Polish Academy of Sciences,Institute of Mathematics
[3] St. Petersburg University,Department of Mathematical Physics, Institute of Physics
来源：
Integral Equations and Operator Theory | 2011年 / 69卷
关键词：
Primary 47B36; Secondary 47A10; 47B25; Jacobi matrix; essential spectrum; gaps; asymptotics;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We give explicit examples of unbounded Jacobi operators with a few gaps in their essential spectrum. More precisely a class of Jacobi matrices whose absolutely continuous spectrum fills any finite number of bounded intervals is considered. Their point spectrum accumulates to +∞ and −∞. The asymptotics of large eigenvalues is also found.
引用
收藏
页码：151 / 170
页数：19
相关论文
共 32 条
  • [11] Janas J.(1992)Subordinacy and spectral theory for infinite matrices Helv. Phys. Acta 65 505-527
  • [12] Malejki M.(1999)Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators Invent. Math. 135 329-367
  • [13] Janas J.(2007)Approximation of eigenvalues of some unbounded self-adjoint discrete Jacobi matrices by eigenvalues of finite submatrices Opuscula Math. 27 37-49
  • [14] Moszyński M.(2003)Spectral properties of some Jacobi matrices with double weights J. Math. Anal. Appl. 280 400-412
  • [15] Janas J.(2002)Absolutely continuous Jacobi operators Proc. Am. Math. Soc. 130 2369-2376
  • [16] Naboko S.(1997)Almost periodic Jacobi matrices with homogeneous spectrum, infinite-dimensional Jacobi inversion, and Hardy spaces of character-automorphic functions J. Geom. Anal. 7 387-435
  • [17] Janas J.(undefined)undefined undefined undefined undefined-undefined
  • [18] Naboko S.(undefined)undefined undefined undefined undefined-undefined
  • [19] Janas J.(undefined)undefined undefined undefined undefined-undefined
  • [20] Naboko S.(undefined)undefined undefined undefined undefined-undefined
1234