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NONCLASSICAL SPECTRAL ASYMPTOTICS AND DIXMIER TRACES: FROM CIRCLES TO CONTACT MANIFOLDS

Heiko Gimperlein ; Magnus Goffeng (Institutionen för matematiska vetenskaper)
FORUM OF MATHEMATICS SIGMA (2050-5094). Vol. 5 (2017), p. Article no e3 .
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: hankel-operators, heisenberg manifolds, integral-operators, connes-dixmier, space, geometry, lipschitz, mappings, formulas, cr



Denna post skapades 2017-08-23.
CPL Pubid: 251346

 

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