Constructs Dixmier traces via eigenvalue sequences in weak Lorentz ideals, gives spectral characterization of measurable operators answering Connes, and applies to nonclassical Weyl laws.
Colin de Verdière, L
4 Pith papers cite this work. Polarity classification is still indexing.
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Proves quantum ergodicity for subLaplacians on contact metric manifolds with ergodic Reeb flow via adapted semiclassical calculus and microlocal projectors.
Eigenfunctions of Baouendi-Grushin and boundary-degenerate elliptic operators satisfy lim sup u_k/k ≤ γ(R^d), the same Pleijel constant as the Dirichlet Laplacian, under weak degeneracy.
Semiclassical Weyl laws and Connes-type integration formulas hold for spectral triples under a weak spectral Condition (W), without prior regularity or dimension restrictions.
citing papers explorer
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Nonclassical Weyl laws and Connes' Integration for weak Lorentz ideals, I
Constructs Dixmier traces via eigenvalue sequences in weak Lorentz ideals, gives spectral characterization of measurable operators answering Connes, and applies to nonclassical Weyl laws.
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Quantum ergodicity for contact metric structures
Proves quantum ergodicity for subLaplacians on contact metric manifolds with ergodic Reeb flow via adapted semiclassical calculus and microlocal projectors.
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Pleijel's theorem for a class of degenerate elliptic operators
Eigenfunctions of Baouendi-Grushin and boundary-degenerate elliptic operators satisfy lim sup u_k/k ≤ γ(R^d), the same Pleijel constant as the Dirichlet Laplacian, under weak degeneracy.
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Noncommutative Geometry, Spectral Asymptotics, and Semiclassical Analysis
Semiclassical Weyl laws and Connes-type integration formulas hold for spectral triples under a weak spectral Condition (W), without prior regularity or dimension restrictions.