A Reproducing Kernel and Toeplitz Operators in the Quantum Plane

zbMath1297.46023arXiv1305.6986MaRDI QIDQ5415930

Stephen Bruce Sontz

Publication date: 19 May 2014

Full work available at URL: https://arxiv.org/abs/1305.6986

zbMATH Keywords

Toeplitz operatorsecond quantizationreproducing kernelquantum planecreation and annihilation operators

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) General quantum mechanics and problems of quantization (81S99) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)

Related Items (6)

Three-dimensional quantum gravity from the quantum pseudo-Kähler plane ⋮ Coherent states for the Manin plane via Toeplitz quantization ⋮ Solutions of nonlinear systems by reproducing kernel method ⋮ Toeplitz Quantization of an Analogue of the Manin Plane ⋮ Toeplitz quantization of the quantum group SU q(2) ⋮ Co-Toeplitz operators and their associated quantization

Cites Work

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• Coherent state quantization of paragrassmann algebras
• On a Hilbert space of analytic functions and an associated integral transform part I
• Paragrassmann algebras as quantum spaces, Part II: Toeplitz Operators
• Paragrassmann Algebras as Quantum Spaces Part I: Reproducing Kernels
• Theory of Reproducing Kernels
• Basic noncommutative geometry

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