A sufficient and sharp criterion for the classical Weyl asymptotic on general complete Riemannian manifolds is the limit of a new invariant c_δ(λ) being zero.
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Semiclassical Weyl laws and Connes integration formulas are obtained for a large class of spectral triples by removing dimension and regularity restrictions and replacing the prior Tauberian condition with a weaker Condition (W).
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The classical Weyl law for Schr\"odinger operators on complete Riemannian manifolds
A sufficient and sharp criterion for the classical Weyl asymptotic on general complete Riemannian manifolds is the limit of a new invariant c_δ(λ) being zero.
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Noncommutative Geometry, Spectral Asymptotics, and Semiclassical Analysis
Semiclassical Weyl laws and Connes integration formulas are obtained for a large class of spectral triples by removing dimension and regularity restrictions and replacing the prior Tauberian condition with a weaker Condition (W).