Functional calculus and quantization commutes with reduction for Toeplitz operators on CR manifolds

2021/12/21 by Andrea Galasso, Galasso, Andrea, Chin-Yu Hsiao +1 · 1 citation
Mathematics · #47B35 (Primary) 32A70 #53D50 (Secondary) #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2112.11257

openalex publication_date 2021/12/21 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

Given a CR manifold with non-degenerate Levi form, we show that the operators of the functional calculus for Toeplitz operators are complex Fourier integral operators of Szegő type. As an application, we establish semi-classical spectral dimensions for Toeplitz operators. We then consider a CR manifold with a compact Lie group action G and we establish quantization commutes with reduction for Toeplitz operators. Moreover, we also compute semi-classical spectral dimensions for G-invariant Toeplitz operators.

Cited by

• Bernstein-Markov measures and Toeplitz theory

Related

• Toeplitz operators on CR manifolds and group actions
• Semi-classical spectral asymptotics of Toeplitz operators on CR manifolds
• Spectral asymptotics of semi-classical Toeplitz operators on Levi non-degenerate CR manifolds
• A Representation Theoretic Approach to Toeplitz Quantization on Flag Manifolds
• Toeplitz operators and Hamiltonian torus action