Remarks on positive definite functions on a group
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929238919086080 |
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| author | Jana, Swapan Pal, Sourav Tomar, Nitin |
| author_facet | Jana, Swapan Pal, Sourav Tomar, Nitin |
| contents | We study the operator-valued positive definite functions on a group using positive block matrices. We give an alternative proof to Brehmer positivity for doubly commuting contractions. We classify all commuting unitary representations over a finite group. We show by examples that the power of a positive-definite function may not be positive definite and also the power of a unitary representation may not be a unitary representation. We also characterize all unitary representations whose powers are also unitary representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06399 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Remarks on positive definite functions on a group Jana, Swapan Pal, Sourav Tomar, Nitin Functional Analysis Operator Algebras We study the operator-valued positive definite functions on a group using positive block matrices. We give an alternative proof to Brehmer positivity for doubly commuting contractions. We classify all commuting unitary representations over a finite group. We show by examples that the power of a positive-definite function may not be positive definite and also the power of a unitary representation may not be a unitary representation. We also characterize all unitary representations whose powers are also unitary representations. |
| title | Remarks on positive definite functions on a group |
| topic | Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2402.06399 |