On the berezin-toeplitz calculus

L. A. Coburn

doi:10.1090/s0002-9939-01-05917-2

On the berezin-toeplitz calculus

L. A. Coburn

Mathematics

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23 Scopus citations

Abstract

We consider the problem of composing Berezin-Toeplitz operators on the Hubert space of Gaussian square-integrable entire functions on complex n-space, Cⁿ. For several interesting algebras of functions on Cⁿ, we have T_hT_ψ = T_◇ψ for all, ψ in the algebra, where T_i is the Berezin-Toeplitz operator associated with and ◇ψ is a "twisted" associative product on the algebra of functions. On the other hand, there is a C^∞ function for which T_h is bounded but T_hT_i ≠ Tψ for any ψ.

Original language	English
Pages (from-to)	3331-3338
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	129
Issue number	11
DOIs	https://doi.org/10.1090/s0002-9939-01-05917-2
State	Published - 2001

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abstract = "We consider the problem of composing Berezin-Toeplitz operators on the Hubert space of Gaussian square-integrable entire functions on complex n-space, Cn. For several interesting algebras of functions on Cn, we have ThTψ = T◇ψ for all, ψ in the algebra, where Ti is the Berezin-Toeplitz operator associated with and ◇ψ is a {"}twisted{"} associative product on the algebra of functions. On the other hand, there is a C∞ function for which Th is bounded but ThTi ≠ Tψ for any ψ.",

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AB - We consider the problem of composing Berezin-Toeplitz operators on the Hubert space of Gaussian square-integrable entire functions on complex n-space, Cn. For several interesting algebras of functions on Cn, we have ThTψ = T◇ψ for all, ψ in the algebra, where Ti is the Berezin-Toeplitz operator associated with and ◇ψ is a "twisted" associative product on the algebra of functions. On the other hand, there is a C∞ function for which Th is bounded but ThTi ≠ Tψ for any ψ.

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On the berezin-toeplitz calculus

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