Toeplitz operators and localization operators
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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.References
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Additional Information
- Miroslav Engliš
- Affiliation: Mathematics Institute, Silesian University at Opava, Na Rybníčku 1, 74601 Opava, Czech Republic – and – Mathematics Institute, Žitná 25, 11567 Prague 1, Czech Republic
- Email: englis@math.cas.cz
- Received by editor(s): July 31, 2006
- Received by editor(s) in revised form: May 7, 2007
- Published electronically: August 18, 2008
- Additional Notes: This research was supported by GA ČR grant no. 201/06/0128 and Ministry of Education research plan no. MSM4781305904.
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 1039-1052
- MSC (2000): Primary 47B35; Secondary 42C40, 32M15, 81R30
- DOI: https://doi.org/10.1090/S0002-9947-08-04547-9
- MathSciNet review: 2452833