Communications in Mathematical Physics

, Volume 271, Issue 1, pp 275–287 | Cite as

Discrete and Embedded Eigenvalues for One-Dimensional Schrödinger Operators

  • Christian RemlingEmail author


I present an example of a discrete Schrödinger operator that shows that it is possible to have embedded singular spectrum and, at the same time, discrete eigenvalues that approach the edges of the essential spectrum (much) faster than exponentially. This settles a conjecture of Simon (in the negative). The potential is of von Neumann-Wigner type, with careful navigation around a previously identified borderline situation.


Nontrivial Solution Asymptotic Formula Essential Spectrum Jacobi Operator Oscillation Theory 
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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of OklahomaNormanUSA

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