On the Berezin-Toeplitz calculus

DOI10.1090/S0002-9939-01-05917-2zbMath0990.47025MaRDI QIDQ2731928

Lewis A. Coburn

Publication date: 30 July 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Segal-Bargmann spaceBerezin-Toeplitz operatorsGaussian square-integrable entire functions

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)

Related Items (18)

Uniformly continuous functions and quantization on the Fock space ⋮ Some weighted estimates for the ∂̅-equation and a finite rank theorem for Toeplitz operators in the Fock space ⋮ Commuting Toeplitz operators on the Segal-Bargmann space ⋮ On an integral representation of the normalized trace of thek-th symmetric tensor power of matrices and some applications ⋮ Complex FIOs and composition of Toeplitz operators ⋮ Cross-Toeplitz operators on the Fock-Segal-Bargmann spaces and two-sided convolutions on the Heisenberg group ⋮ COMPACT OPERATORS AND THE PLURIHARMONIC BEREZIN TRANSFORM ⋮ Commuting Toeplitz operators with quasi-homogeneous symbols on the Segal-Bargmann space ⋮ Algebraic properties and the finite rank problem for Toeplitz operators on the Segal-Bargmann space ⋮ Finite rank perturbations of Toeplitz products on the Bergman space ⋮ Commutators and semi-commutators of Toeplitz operators on the Fock space ⋮ Heat flow and an algebra of Toeplitz operators ⋮ The finite rank theorem for Toeplitz operators on the Fock space ⋮ Commutative \(C^{\ast}\)-algebras of Toeplitz operators and quantization on the unit disk ⋮ Toeplitz operators and localization operators ⋮ Commutants of Toeplitz operators with separately radial polynomial symbols ⋮ Berezin--Toeplitz quantization and composition formulas ⋮ Self-adjointness of Toeplitz operators on the Segal-Bargmann space

Cites Work

• Quantum Riemann surfaces. I: The unit disc
• The measure algebra of the Heisenberg group
• Toeplitz operators in \(n\)-dimensions
• On the deformation of rings and algebras. III
• Toeplitz Operators on the Segal-Bargmann Space
• On a Hilbert space of analytic functions and an associated integral transform part I
• Harmonic Analysis in Phase Space. (AM-122)
• Heat Flow and Berezin-Toeplitz Estimates

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