• Corpus ID: 235352878

Semiclassical Weyl law and exact spectral asymptotics in noncommutative geometry

@inproceedings{Mcdonald2021SemiclassicalWL,
  title={Semiclassical Weyl law and exact spectral asymptotics in noncommutative geometry},
  author={Edward Mcdonald and Fedor Sukochev and Dmitriy Zanin},
  year={2021}
}

• E. Mcdonald, F. Sukochev, D. Zanin
• Published 4 June 2021
• Mathematics

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 lim h↓0 hTr(χ(−∞,0)(h D + V )) = − ∫ V p 2 − |ds| .