Christian Remling
Discrete and embedded eigenvalues for one-dimensional Schr"odinger operators
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ABSTRACT.  I present an example of a discrete Schr"odinger 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.