The function-operator convolution algebra over the Bergman space of the ball and its Gelfand theory
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909979004370944 |
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| author | Dewage, Vishwa Fulsche, Robert Ólafsson, Gestur |
| author_facet | Dewage, Vishwa Fulsche, Robert Ólafsson, Gestur |
| contents | We investigate the structure of the commutative Banach algebra formed as the direct sum of integrable radial functions on the disc and the radial operators on the Bergman space, endowed with the convolution from quantum harmonic analysis as the product. In particular, we study the Gelfand theory of this algebra and discuss certain properties of the appropriate Fourier transform of operators which naturally arises from the Gelfand transform. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24746 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The function-operator convolution algebra over the Bergman space of the ball and its Gelfand theory Dewage, Vishwa Fulsche, Robert Ólafsson, Gestur Functional Analysis We investigate the structure of the commutative Banach algebra formed as the direct sum of integrable radial functions on the disc and the radial operators on the Bergman space, endowed with the convolution from quantum harmonic analysis as the product. In particular, we study the Gelfand theory of this algebra and discuss certain properties of the appropriate Fourier transform of operators which naturally arises from the Gelfand transform. |
| title | The function-operator convolution algebra over the Bergman space of the ball and its Gelfand theory |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2512.24746 |