Eigenvalues of singular measures and Connes' noncommutative integration.
Journal article, 2022

In a domain Ω⊂R^N we consider compact, Birman–Schwinger type operators of the form T​=A^∗P A with P being a Borel measure in Ω, containing a singular part, andA being an order −N/2 pseudodifferential operator. Operators are defined by means of quadratic forms. For a class of such operators, we obtain a proper version of H. Weyl's law for eigenvalues, with order not depending on dimensional characteristics of the measure. These results lead to establishing measurability, in the sense of Dixmier–Connes, of such operators and the noncommutative version of integration over Lipschitz surfaces and rectifiable sets.

Connes integration

Design for manufacturing, welding, tolerance, robust design

Weyl law

eigenvalue asymptotics

singular measures


Grigori Rozenblioum

Chalmers, Mathematical Sciences

Euler International Mathematical Institute

Journal of Spectral Theory

1664-039X (ISSN) 1664-0403 (eISSN)

Vol. 12 1 259-300

Subject Categories

Mathematical Analysis



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1/3/2023 1