We present upper estimates for the number of negative eigenvalues of two-dimensional Schrödinger operators with potentials generated by Ahlfors regular measures of arbitrary fractional dimension α ∈ (0, 2]. The estimates are given in terms of integrals of the potential with a logarithmic weight and of its L log L type Orlicz norms. In the case α = 1, our results are stronger than the known ones about Schrödinger operators with potentials supported by Lipschitz curves.
In this paper, we extend the well known estimates for the number of negative eigenvalues of one-dimensional Schrodinger operators with potentials that are absolutely continuous with respect to the Lebesgue measure to the case of strongly singular potentials.
This paper is concerned with the estimation of the number of negative eigenvalues (bound states) of Schrödinger operators in a strip subject to Neumann boundary conditions. The estimates involve weighted L 1 norms and L ln L norms of the potential. Estimates involving the norms of the potential supported by a curve embedded in a strip are also presented.
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