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Toeplitz operators and localization operators

Author(s): Miroslav Englis
Journal: Trans. Amer. Math. Soc. 361 (2009), 1039-1052.
MSC (2000): Primary 47B35; Secondary 42C40, 32M15, 81R30
Posted: August 18, 2008
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Abstract: We show that for any localization operator on the Fock space with polynomial window, there exists a constant coefficient linear partial differential operator $ D$ such that the localization operator with symbol $ f$ coincides with the Toeplitz operator with symbol $ Df$. An analogous result also holds in the context of Bergman spaces on bounded symmetric domains. This verifies a recent conjecture of Coburn and simplifies and generalizes recent results of Lo.

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Additional Information:

Miroslav Englis
Affiliation: Mathematics Institute, Silesian University at Opava, Na Rybnícku 1, 74601 Opava, Czech Republic - and - Mathematics Institute, Zitná 25, 11567 Prague 1, Czech Republic
Email: englis@math.cas.cz

DOI: 10.1090/S0002-9947-08-04547-9
PII: S 0002-9947(08)04547-9
Keywords: Toeplitz operator, localization operator, bounded symmetric domain, Segal-Bargmann space, Bergman space
Received by editor(s): July 31, 2006
Received by editor(s) in revised form: May 7, 2007
Posted: August 18, 2008
Additional Notes: This research was supported by~GA CR grant no.~201/06/0128 and Ministry of Education research plan no.~MSM4781305904.
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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