Aleksey Kostenko
Weyl-Titchmarsh Theory for Schroedinger Operators with Strongly Singular Potentials.
Fri, 07/02/2010 - 15:01 — SomNambulAuthors: Aleksey Kostenko, Alexander Sakhnovich, Gerald Teschl
Subjects: Spectral Theory
AbstractWe develop Weyl-Titchmarsh theory for Schroedinger operators with strongly
singular potentials such as perturbed spherical Schroedinger operators (also
known as Bessel operators). It is known that in such situations one can still
define a corresponding singular Weyl m-function and it was recently shown that
there is also an associated spectral transformation. Here we will give a
general criterion when the singular Weyl function can be analytically extended
to the upper half plane.1--D Schr\"odinger operators with local interactions on a discrete set.
Wed, 08/26/2009 - 14:58 — SomNambulAuthors: Aleksey Kostenko, Mark Malamud
Subjects: Spectral Theory
AbstractSpectral properties of 1-D Schr\"odinger operators
$\mathrm{H}_{X,\alpha}:=-\frac{\mathrm{d}^2}{\mathrm{d} x^2} + \sum_{x_{n}\in
X}\alpha_n\delta(x-x_n)$ with local point interactions on a discrete set
$X=\{x_n\}_{n=1}^\infty$ are well studied when
$d_*:=\inf_{n,k\in\N}|x_n-x_k|>0$. Our paper is devoted to the case $d_*=0$. We
consider $\mathrm{H}_{X,\alpha}$ in the framework of extension theory of
symmetric operators by applying the technique of boundary triplets and the
corresponding Weyl functions.
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