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JOURNALS // Funktsional'nyi Analiz i ego Prilozheniya // Archive
Funktsional. Anal. i Prilozhen., 2023 Volume 57, Issue 1, Pages 52–76 (Mi faa4025)
This article is cited in 2 papers

Connes integration formula: a constructive approach

D. V. Zanin, F. A. Sukochev

University of New South Wales, School of Mathematics and Statistics

Abstract: 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.

Received: 14.06.2022
Revised: 12.08.2022
Accepted: 06.10.2022

DOI: 10.4213/faa4025


 English version: Functional Analysis and Its Applications, 2023, 57:1, 40–59

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© Steklov Math. Inst. of RAS, 2025