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• W2901119135 abstract "The goal of this paper is the spectral analysis of the Schrodinger type operator $H=L+V$, the perturbation of the Taibleson-Vladimirov multiplier $L=mathfrak{D}^{alpha}$ by a potential $V$. Assuming that $V$ belongs to a certain class of potentials we show that the discrete part of the spectrum of $H$ may contain negative energies, it also appears in the spectral gaps of $L$. We will split the spectrum of $H$ in two parts: high energy part containing eigenvalues which correspond to the eigenfunctions located on the support of the potential $V,$ and low energy part which lies in the spectrum of certain bounded Schrodinger-type operator acting on the Dyson hierarchical lattice. We pay special attention to the class of sparse potentials. In this case we obtain precise spectral asymptotics for $H$ provided the sequence of distances between locations tends to infinity fast enough. We also obtain certain results concerning localization theory for $H$ subject to (non-ergodic) random potential $V$. Examples illustrate our approach." @default.
• W2901119135 created "2018-11-29" @default.
• W2901119135 creator A5008846261 @default.
• W2901119135 creator A5027970631 @default.
• W2901119135 creator A5081868613 @default.
• W2901119135 date "2018-11-13" @default.
• W2901119135 modified "2023-10-14" @default.
• W2901119135 title "On the spectrum of the hierarchical Schroedinger operator" @default.
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• W2901119135 hasPublicationYear "2018" @default.
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