TY - JOUR
T1 - The Negative Spectrum of Schrödinger Operators with Fractal Potentials
JO - Analysis in Theory and Applications
VL - 4
SP - 381
EP - 393
PY - 2017
DA - 2017/10
SN - 31
DO - http://doi.org/10.4208/ata.2015.v31.n4.4
UR - https://global-sci.org/intro/article_detail/ata/4646.html
KW - Anisotropic function space, anisotropic fractal, Schrödinger operators, negative eigenvalues.
AB - <p style="text-align: justify;">Let $Γ ⊂ \mathbb{R}^2$ be a regular anisotropic fractal. We discuss the problem of the
negative 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 Laplanian
in $\mathbb{R}^2$ and $tr^Γ_b$ is a fractal potential (distribution) supported by $Γ$.</p>