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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.11697 |
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| _version_ | 1866908471864066048 |
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| author | Chang, Chin-Chia Herrmann, Hendrik Hsiao, Chin-Yu |
| author_facet | Chang, Chin-Chia Herrmann, Hendrik Hsiao, Chin-Yu |
| contents | Let $X$ be a compact strictly pseudoconvex embeddable CR manifold and let $A$ be the Toeplitz operator on $X$ associated with a Reeb vector field $\mathcal{T}\in\mathscr{C}^\infty(X,TX)$. Consider the operator $χ_k(A)$ defined by functional calculus of $A$, where $χ$ is a smooth function with compact support in the positive real line and $χ_k(λ):=χ(k^{-1}λ)$. It was established recently that $χ_k(A)(x,y)$ admits a full asymptotic expansion in $k$. The second coefficient of the expansion plays an important role in the further study of CR geometry. In this work, we calculate the second coefficient of the expansion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11697 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the second coefficient in the semi-classical expansion of Toeplitz Operators Chang, Chin-Chia Herrmann, Hendrik Hsiao, Chin-Yu Complex Variables Differential Geometry Let $X$ be a compact strictly pseudoconvex embeddable CR manifold and let $A$ be the Toeplitz operator on $X$ associated with a Reeb vector field $\mathcal{T}\in\mathscr{C}^\infty(X,TX)$. Consider the operator $χ_k(A)$ defined by functional calculus of $A$, where $χ$ is a smooth function with compact support in the positive real line and $χ_k(λ):=χ(k^{-1}λ)$. It was established recently that $χ_k(A)(x,y)$ admits a full asymptotic expansion in $k$. The second coefficient of the expansion plays an important role in the further study of CR geometry. In this work, we calculate the second coefficient of the expansion. |
| title | On the second coefficient in the semi-classical expansion of Toeplitz Operators |
| topic | Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2412.11697 |