- Nonclassical spectral asymptotics and Dixmier traces: From circles to contact manifolds(arXiv)
Writer : Heiko Gimperlein, Magnus Goffeng
Summary : We take into account the spectral habits and noncommutative geometry of commutators [P,f], the place P is an operator of order 0 with geometric origin and f a multiplication operator by a perform. When f is Hölder steady, the spectral asymptotics is ruled by singularities. We examine exact spectral asymptotics by means of the computation of Dixmier traces; such computations have solely been thought-about in much less singular settings. Despite the fact that a Weyl regulation fails for these operators, and no pseudo-differential calculus is offered, variations of Connes’ residue hint theorem and associated integral formulation proceed to carry. On the circle, a big class of non-measurable Hankel operators is obtained from Hölder steady features f, displaying a variety of nonclassical spectral asymptotics past the Weyl regulation. The outcomes lengthen from Riemannian manifolds to contact manifolds and noncommutative tori.
2. Hankel operators and the Dixmier hint on the Hardy house(arXiv)
Writer : Miroslav Engliš, Genkai Zhang
Summary : We give standards for the membership of Hankel operators on the Hardy house on the disc within the Dixmier class, and set up estimates for his or her Dixmier hint. In distinction to the scenario within the Bergman house setting, it seems that there exist Dixmier-class Hankel operators which aren’t measurable (i.e. their Dixmier hint is determined by the selection of the underlying Banach restrict), in addition to Dixmier-class Hankel operators which don’t belong to the (1,∞) Schatten-Lorentz preferrred. A associated query regarding logarithmic interpolation of Besov areas can also be mentioned.
