Eigenvalues of singular measures and Connes’ noncommutative integration
Artikel i vetenskaplig tidskrift, 2022
the form T_{P;A}= A^*P A with P being a Borel measure in \Omega containing a singular part,
and A 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
noncommutative integation
singular measures
Författare
Grigori Rozenblioum
Chalmers, Matematiska vetenskaper
Journal of Spectral Theory
1664-039X (ISSN) 1664-0403 (eISSN)
Vol. 12 1 259-300Ämneskategorier
Matematisk analys
DOI
10.4171/JST/401