Journal of Operator Theory
Volume 72, Issue 1, Summer 2014 pp. 241-256.
Classe de Dixmier d'operateurs de Hankel
Authors:
Romaric Tytgat
Author institution: LATP, U.M.R. C.N.R.S. 7353, CMI,
Universite de Provence, 39 Rue F-Joliot-Curie,
13453 Marseille Cedex 13, France
Summary: Let $s$ be a non-vanishing Stieltjes moment sequence
and let $\mu$ be a
representing measure of it. We denote by $\mu_{1}$ the image measure in $\C$
of $\mu \otimes \sigma$ under the map $(t,\xi) \mapsto \sqrt{t}\xi$, when
$\sigma$ is the rotation invariant probability measure on the unit sphere
and
we study Hankel operator with anti-holomorphic symbol. We characterize the
Dixmier space and compute the Dixmier trace for $\mathrm d\mu=\mathrm
e^{-\Psi(x)}\mathrm dx$. We study the examples $\Psi(x)=\mathrm e^{x^{j}}$,
$j>0$ or $\Psi(x)=\mathrm e^{\mathrm e^{x}}$.
DOI: http://dx.doi.org/10.7900/jot.2012dec19.1987
Keywords: Dixmier trace, Hankel operators
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