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Volume 31, Issue 4
The Negative Spectrum of Schrödinger Operators with Fractal Potentials

B. Wu, H. Y. Wang & W. Y. Su

Anal. Theory Appl., 31 (2015), pp. 381-393.

Published online: 2017-10

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  • Abstract

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 $Γ$.

  • Keywords

Anisotropic function space, anisotropic fractal, Schrödinger operators, negative eigenvalues.

  • AMS Subject Headings

47G30, 58J50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-31-381, author = {}, title = {The Negative Spectrum of Schrödinger Operators with Fractal Potentials}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {31}, number = {4}, pages = {381--393}, abstract = {

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 $Γ$.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2015.v31.n4.4}, url = {http://global-sci.org/intro/article_detail/ata/4646.html} }
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 -

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 $Γ$.

B. Wu, H. Y. Wang & W. Y. Su. (1970). The Negative Spectrum of Schrödinger Operators with Fractal Potentials. Analysis in Theory and Applications. 31 (4). 381-393. doi:10.4208/ata.2015.v31.n4.4
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