Nonclassical Spectral Asymptotics and Dixmier Traces: from Circles to Contact Manifolds
Artikel i vetenskaplig tidskrift, 2017

We consider the spectral behavior and noncommutative geometry of commutators [P, f], where P is an operator of order 0 with geometric origin and f a multiplication operator by a function. When f is Holder continuous, the spectral asymptotics is governed by singularities. We study precise spectral asymptotics through the computation of Dixmier traces; such computations have only been considered in less singular settings. Even though a Weyl law fails for these operators, and no pseudodifferential calculus is available, variations of Connes' residue trace theorem and related integral formulas continue to hold. On the circle, a large class of nonmeasurable Hankel operators is obtained from Holder continuous functions f, displaying a wide range of nonclassical spectral asymptotics beyond the Weyl law. The results extend from Riemannian manifolds to contact manifolds and noncommutative tori.

space

formulas

mappings

cr

geometry

heisenberg manifolds

connes-dixmier

lipschitz

integral-operators

hankel-operators

Författare

Heiko Gimperlein

Magnus C H T Goffeng

Chalmers, Matematiska vetenskaper

Göteborgs universitet

FORUM OF MATHEMATICS SIGMA

2050-5094 (ISSN)

Vol. 5 Article no e3 -

Ämneskategorier

Matematik

Geometri

Matematisk analys

Fundament

Grundläggande vetenskaper

DOI

10.1017/fms.2016.33

Mer information

Skapat

2017-10-08