Geodesic
Connes integration formula: a constructive approach
Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 1, pp. 52-76

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A version of Connes Integration Formula which provides concrete asymptotics of eigenvalues is given. This radically extends the class of quantum-integrable functions on compact Riemannian manifolds.
Keywords: Connes integration formula, compact $d$-dimensional Riemannian manifold, Birman–Solomyak asymptotic formula. 
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D. V. Zanin; F. A. Sukochev. Connes integration formula: a constructive approach. Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 1, pp. 52-76. http://geodesic.mathdoc.fr/item/FAA_2023_57_1_a3/