SCHRÖDINGER OPERATORS ON HOMOGENEOUS METRIC TREES: SPECTRUM IN GAPS
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Publication:4420441
DOI10.1142/S0129055X02001235zbMath1038.81023arXivmath/0109016OpenAlexW1986509210MaRDI QIDQ4420441
Alexander V. Sobolev, Michael Solomyak
Publication date: 17 August 2003
Published in: Reviews in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0109016
Applications of operator theory in the physical sciences (47N50) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Perturbation theories for operators and differential equations in quantum theory (81Q15) Discrete potential theory (31C20)
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Cites Work
- On the existence of eigenvalues of the Schrödinger operator H-\(\lambda\) W in a gap of \(\sigma\) (H)
- Eigenvalue branches of the Schrödinger operator H-\(\lambda\) W in a gap of \(\sigma\) (H)
- Discrete spectrum of the perturbed Dirac operator
- Scattering on the Bruhat-Tits tree. I
- A MOURRE ESTIMATE FOR A SCHRÖDINGER OPERATOR ON A BINARY TREE
- On the Eigenvalue Behaviour for a Class of Differential Operators on Semiaxis
- Eigenvalue Estimates for the Weighted Laplacian on Metric Trees
- Spectral Asymptotics, Renewal Theorem, and the Berry Conjecture for a Class of Fractals
- [https://portal.mardi4nfdi.de/wiki/Publication:4893803 The negative discrete spectrum of a two-dimensional Schr�dinger operator]