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 asymptotics for the dimension of the spectral spaces of 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 asymptotics for the dimension of the spectral spaces of G-invariant Toeplitz operators.

Galasso, A., Hsiao, C. (2024). Functional calculus and quantization commutes with reduction for Toeplitz operators on CR manifolds. MATHEMATISCHE ZEITSCHRIFT, 308(1) [10.1007/s00209-024-03561-1].

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

Galasso, A;
2024

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 asymptotics for the dimension of the spectral spaces of 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 asymptotics for the dimension of the spectral spaces of G-invariant Toeplitz operators.
Articolo in rivista - Articolo scientifico
32A25; 32Vxx; 53D50; CR manifolds; Group actions; Toeplitz operators;
English
27-lug-2024
2024
308
1
5
none
Galasso, A., Hsiao, C. (2024). Functional calculus and quantization commutes with reduction for Toeplitz operators on CR manifolds. MATHEMATISCHE ZEITSCHRIFT, 308(1) [10.1007/s00209-024-03561-1].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/499399
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