The Negative Spectrum of Schrödinger Operators with Fractal Potentials (Analysis in Theory and Applications, 2017)
Let $Γ ⊂ \mathbb{R}^2$ be a regular anisotropic fractal. We discuss the problem of thenegative spectrum for the Schrödinger operators associated with the formal expression $$H_β =id−∆+βtr^Γ_b, β∈R,$$ acting in the anisotropic Sobolev space $W^{1,α}_2(\mathbb{R}^2)$, where $∆$ is the Dirichlet Laplanianin $\mathbb{R}^2$ and $tr^Γ_b$ is a fractal potential (distribution) supported by $Γ$.