Spectral asymptotics of semi-classical Toeplitz operators on Levi non-degenerate CR manifolds
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918025178906624 |
|---|---|
| author | Shen, Wei-Chuan |
| author_facet | Shen, Wei-Chuan |
| contents | We consider any compact CR manifold whose Levi form is non-degenerate of constant signature $(n_-,n_+)$, $n_-+n_+=n$. For $λ>0$ and $q\in\{0,\cdots,n\}$, we let $Π_λ^{(q)}$ be the spectral projection of the Kohn Laplacian of $(0,q)$-forms corresponding to the interval $[0,λ]$. For certain classical pseudodifferential operators $P$, we study a class of generalized elliptic Toeplitz operators $T_{P,λ}^{(q)}:=Π_λ^{(q)}\circ P\circ Π_λ^{(q)}$. For any cut-off $χ\in\mathscr C^\infty_c(\mathbb R\setminus\{0\})$, we establish the full asymptotics of the semi-classical spectral projector $χ(k^{-1}T_{P,λ}^{(q)})$ as $k\to+\infty$. Our main result conclude that the smooth Schwartz kernel $χ(k^{-1}T_{P,λ}^{(n_-)})(x,y)$ is the sum of two semi-classical oscillatory integrals with complex-valued phase functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13014 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral asymptotics of semi-classical Toeplitz operators on Levi non-degenerate CR manifolds Shen, Wei-Chuan Complex Variables Analysis of PDEs Spectral Theory 32V30, 32T15, 58J40 We consider any compact CR manifold whose Levi form is non-degenerate of constant signature $(n_-,n_+)$, $n_-+n_+=n$. For $λ>0$ and $q\in\{0,\cdots,n\}$, we let $Π_λ^{(q)}$ be the spectral projection of the Kohn Laplacian of $(0,q)$-forms corresponding to the interval $[0,λ]$. For certain classical pseudodifferential operators $P$, we study a class of generalized elliptic Toeplitz operators $T_{P,λ}^{(q)}:=Π_λ^{(q)}\circ P\circ Π_λ^{(q)}$. For any cut-off $χ\in\mathscr C^\infty_c(\mathbb R\setminus\{0\})$, we establish the full asymptotics of the semi-classical spectral projector $χ(k^{-1}T_{P,λ}^{(q)})$ as $k\to+\infty$. Our main result conclude that the smooth Schwartz kernel $χ(k^{-1}T_{P,λ}^{(n_-)})(x,y)$ is the sum of two semi-classical oscillatory integrals with complex-valued phase functions. |
| title | Spectral asymptotics of semi-classical Toeplitz operators on Levi non-degenerate CR manifolds |
| topic | Complex Variables Analysis of PDEs Spectral Theory 32V30, 32T15, 58J40 |
| url | https://arxiv.org/abs/2505.13014 |