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In this note, under a certain assumption on an affine space of operators, which admit embedded eigenvalues, it is shown that the singular part of the spectral shift function of any pair of operators from this space is an integer-valued function. The proof uses a natural decomposition of Pushnitskis $mu$-invariant into absolutely continuous and singular parts. As a corollary, the Birman-Krein formula follows.
We consider non-local Schrodinger operators with kinetic terms given by several different types of functions of the Laplacian and potentials decaying to zero at infinity, and derive conditions ruling embedded eigenvalues out. These results contrast a
We revisit an archive submission by P. B. Denton, S. J. Parke, T. Tao, and X. Zhang, arXiv:1908.03795, on $n times n$ self-adjoint matrices from the point of view of self-adjoint Dirichlet Schrodinger operators on a compact interval.
We consider a Schrodinger operator with complex-valued potentials on the line. The operator has essential spectrum on the half-line plus eigenvalues (counted with algebraic multiplicity) in the complex plane without the positive half-line. We determi
The present work aims at obtaining estimates for transformation operators for one-dimensional perturbed radial Schrodinger operators. It provides more details and suitable extensions to already existing results, that are needed in other recent contributions dealing with these kinds of operators.
In this article, we consider the semiclassical Schrodinger operator $P = - h^{2} Delta + V$ in $mathbb{R}^{d}$ with confining non-negative potential $V$ which vanishes, and study its low-lying eigenvalues $lambda_{k} ( P )$ as $h to 0$. First, we giv