Functional calculus and quantization commutes with reduction for Toeplitz operators on CR manifolds
Functional Analysis
2022-08-10 v4 Complex Variables
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 Szeg\H{o} 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 and we establish quantization commutes with reduction for Toeplitz operators. Moreover, we also compute semi-classical spectral dimensions for -invariant Toeplitz operators.
Keywords
Cite
@article{arxiv.2112.11257,
title = {Functional calculus and quantization commutes with reduction for Toeplitz operators on CR manifolds},
author = {Andrea Galasso and Chin-Yu Hsiao},
journal= {arXiv preprint arXiv:2112.11257},
year = {2022}
}
Comments
Typos corrected, bibliographic item added. arXiv admin note: text overlap with arXiv:2108.11061; text overlap with arXiv:2011.09124 by other authors