Toeplitz operators and localization operators

Engliš, Miroslav

doi:10.1090/S0002-9947-08-04547-9

Toeplitz operators and localization operators
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by Miroslav Engliš PDF

Trans. Amer. Math. Soc. 361 (2009), 1039-1052 Request permission

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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