Operators in the Fock-Toeplitz algebra
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910465591869440 |
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| author | Bauer, Wolfram Fulsche, Robert Rodriguez, Miguel Angel Rodriguez |
| author_facet | Bauer, Wolfram Fulsche, Robert Rodriguez, Miguel Angel Rodriguez |
| contents | We consider various classes of bounded operators on the Fock space $F^2$ of Gaussian square integrable entire functions over the complex plane. These include Toeplitz (type) operators, weighted composition operators, singular integral operators, Volterra-type operators and Hausdorff operators and range from classical objects in harmonic analysis to more recently introduced classes. As a leading problem and closely linked to well-known compactness characterizations we pursue the question of when these operators are contained in the Toeplitz algebra. This paper combines a (certainly in-complete) survey of the classical and more recent literature including new ideas for proofs from the perspective of quantum harmonic analysis (QHA). Moreover, we have added a number of new theorems and links between known results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20792 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Operators in the Fock-Toeplitz algebra Bauer, Wolfram Fulsche, Robert Rodriguez, Miguel Angel Rodriguez Functional Analysis 30H20, 46E22, 47B35, 47B33 We consider various classes of bounded operators on the Fock space $F^2$ of Gaussian square integrable entire functions over the complex plane. These include Toeplitz (type) operators, weighted composition operators, singular integral operators, Volterra-type operators and Hausdorff operators and range from classical objects in harmonic analysis to more recently introduced classes. As a leading problem and closely linked to well-known compactness characterizations we pursue the question of when these operators are contained in the Toeplitz algebra. This paper combines a (certainly in-complete) survey of the classical and more recent literature including new ideas for proofs from the perspective of quantum harmonic analysis (QHA). Moreover, we have added a number of new theorems and links between known results. |
| title | Operators in the Fock-Toeplitz algebra |
| topic | Functional Analysis 30H20, 46E22, 47B35, 47B33 |
| url | https://arxiv.org/abs/2405.20792 |