Abstract
The classical Cwikel-Lieb-Rozenblum and Lieb-Thirring inequalities in their general form allow one to estimate the number of negative eigenvalues N = #{λ i < 0} and the sums S γ = ∑|λ i |γ for a wide class of Schrödinger operators. We will present here some new examples (Anderson Hamiltonian, operators on lattices, quantum graphs and groups). In some cases below, the parabolic semigroup has an exponential fractional decay at t→∞. This makes it possible to consider potentials decaying very slowly (logarithmical) at infinity. We also will discuss the case of small local dimension of the underlying manifold, which is usually not covered by the general theory.
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Molchanov, S., Vainberg, B. (2009). On Negative Spectrum of Schrödinger Type Operators. In: Cialdea, A., Ricci, P.E., Lanzara, F. (eds) Analysis, Partial Differential Equations and Applications. Operator Theory: Advances and Applications, vol 193. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9898-9_15
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DOI: https://doi.org/10.1007/978-3-7643-9898-9_15
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