Toeplitz operators and group-moment coordinates for quasi-elliptic and quasi-hyperbolic symbols
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910418415386624 |
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| author | Quiroga-Barranco, Raul Sanchez-Nungaray, Armando |
| author_facet | Quiroga-Barranco, Raul Sanchez-Nungaray, Armando |
| contents | For $\mathbb{B}^n$ the $n$-dimensional unit ball and $D_n$ its Siegel unbounded realization, we consider Toeplitz operators acting on weighted Bergman spaces with symbols invariant under the actions of the maximal Abelian subgroups of biholomorphisms $\mathbb{T}^n$ (quasi-elliptic) and $\mathbb{T}^n \times \mathbb{R}_+$ (quasi-hyperbolic). Using geometric symplectic tools (Hamiltonian actions and moment maps) we obtain simple diagonalizing spectral integral formulas for such kinds of operators. Some consequences show how powerful the use of our differential geometric methods are. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14582 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Toeplitz operators and group-moment coordinates for quasi-elliptic and quasi-hyperbolic symbols Quiroga-Barranco, Raul Sanchez-Nungaray, Armando Functional Analysis Operator Algebras Primary 47B35, 32A36, Secondary 53D20 For $\mathbb{B}^n$ the $n$-dimensional unit ball and $D_n$ its Siegel unbounded realization, we consider Toeplitz operators acting on weighted Bergman spaces with symbols invariant under the actions of the maximal Abelian subgroups of biholomorphisms $\mathbb{T}^n$ (quasi-elliptic) and $\mathbb{T}^n \times \mathbb{R}_+$ (quasi-hyperbolic). Using geometric symplectic tools (Hamiltonian actions and moment maps) we obtain simple diagonalizing spectral integral formulas for such kinds of operators. Some consequences show how powerful the use of our differential geometric methods are. |
| title | Toeplitz operators and group-moment coordinates for quasi-elliptic and quasi-hyperbolic symbols |
| topic | Functional Analysis Operator Algebras Primary 47B35, 32A36, Secondary 53D20 |
| url | https://arxiv.org/abs/2404.14582 |