On Algebras of Functions over Infinite Dimensions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914528214646784 |
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| author | Giannakis, Dimitrios Jebelli, Mohammad Javad Latifi Montgomery, Michael |
| author_facet | Giannakis, Dimitrios Jebelli, Mohammad Javad Latifi Montgomery, Michael |
| contents | We introduce a family of reproducing kernel Hilbert spaces $\mathcal A_Λ$ of holomorphic functions defined on an infinite--dimensional domain in a separable Hilbert space, $\mathbb{H}$. The reproducing kernel of $\mathcal A_Λ$ is constructed using the covariance operator associated with a Gaussian measure on $\mathbb{H}$, along with a holomorphic function $Λ$ on the unit disk. Under certain conditions on the kernel, $\mathcal A_Λ$ is closed under pointwise multiplication, giving it the structure of a reproducing kernel Hilbert algebra (RKHA). We also study twisted canonical commutation relations on these RKHAs, where the creation and annihilation operators are both bounded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02816 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Algebras of Functions over Infinite Dimensions Giannakis, Dimitrios Jebelli, Mohammad Javad Latifi Montgomery, Michael Mathematical Physics Complex Variables 46E50, 46E22, 32A38, 81S05 We introduce a family of reproducing kernel Hilbert spaces $\mathcal A_Λ$ of holomorphic functions defined on an infinite--dimensional domain in a separable Hilbert space, $\mathbb{H}$. The reproducing kernel of $\mathcal A_Λ$ is constructed using the covariance operator associated with a Gaussian measure on $\mathbb{H}$, along with a holomorphic function $Λ$ on the unit disk. Under certain conditions on the kernel, $\mathcal A_Λ$ is closed under pointwise multiplication, giving it the structure of a reproducing kernel Hilbert algebra (RKHA). We also study twisted canonical commutation relations on these RKHAs, where the creation and annihilation operators are both bounded. |
| title | On Algebras of Functions over Infinite Dimensions |
| topic | Mathematical Physics Complex Variables 46E50, 46E22, 32A38, 81S05 |
| url | https://arxiv.org/abs/2605.02816 |