@Article{Lotoreichik2011,
author = "Lotoreichik, Vladimir",
title = "Singular continuous spectrum of half-line Schrödinger operators with point interactions on a sparse set",
journal = "Opuscula Math.",
year = "2011",
volume = "31",
number = "4",
pages = "615--628",
doi = "http://dx.doi.org/10.7494/OpMath.2011.31.4.615",
url = "http://dx.doi.org/10.7494/OpMath.2011.31.4.615",
abstract = "We say that a discrete set \(X = \{ x_n \}_{n\in \mathbb{N}_0}\) on the half-line \[0 = x_0 \lt x_1 \lt x_2 \lt x_3 \lt ... \lt x_n \lt ... \lt +\infty \] is sparse if the distances \(\Delta x_n = x_{n+1}- x_n\) between neighbouring points satisfy the condition \(\frac{\Delta x_n}{\Delta x_{n-1}} \to +\infty\). In this paper half-line Schrödinger operators with point \(\delta\)- and \(\delta'\)-interactions on a sparse set are considered. Assuming that strengths of point interactions tend to \(\infty\) we give simple sufficient conditions for such Schrödinger operators to have non-empty singular continuous spectrum and to have purely singular continuous spectrum, which coincides with \(\mathbb{R}_+\).",
keywords = "half-line Schrödinger operators, \(\delta\)-interactions, \(\delta '\)-interactions, singular continuous spectrum",
issn = "1232-9274"
}