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The CLR Inequality for Dominated Semigroups

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Abstract

The Cwikel-Lieb-Rozenbljum inequality estimating the number of bound states of a quantum Hamiltonian operator is proved for semigroups \(S(t) = \mathrm {e}_{0}^{-tH}\), \(t\geqslant 0\), on L 2(μ) for a σ-finite measure μ, such that S is dominated by a semigroup |S| of point wise positive operators on L 2(μ).

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  1. School of Mathematics, The University of New South Wales, NSW, 2052, Sydney, Australia

    Brian Jefferies

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  1. Brian Jefferies
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Jefferies, B. The CLR Inequality for Dominated Semigroups. Math Phys Anal Geom 17, 115–137 (2014). https://doi.org/10.1007/s11040-014-9145-6

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