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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 $\Psi(x)=\mathrm e^{\mathrm e^{x}}$.

Keywords: Dixmier trace, Hankel operators

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