Semiclassical Weyl law and exact spectral asymptotics in noncommutative geometry
Edward McDonald,
Fedor Sukochev,
Dmitriy Zanin
Abstract:We prove a Tauberian theorem for singular values of noncommuting operators which allows us to prove exact asymptotic formulas in noncommutative geometry at a high degree of generality. We explain how, via the Birman-Schwinger principle, these asymptotics imply that a semiclassical Weyl law holds for many interesting noncommutative examples. In Connes' notation for quantized calculus, we prove that for a wide class of p-summable spectral triples (A, H, D) and self-adjoint V ∈ A, there holds
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