Grushin Operator on Infinite Dimensional Homogeneous Lie Groups
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908605064675328 |
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| author | Egwe, M. E. Opadara, J. I. |
| author_facet | Egwe, M. E. Opadara, J. I. |
| contents | A collection of infinite dimensional complete vector fields $\left\{V_i\right\}_{i=1}^{\infty}$ acting on a locally convex manifolds $M$ on which a smooth positive measure $μ$ is defined was considered. It was assumed that the vector fields generates an infinite dimensional Lie algebra $\mathfrak{g}$ and satisfies H$\ddot{o}$rmander's condition. The sum of squares of Grushin operators related to the vector fields was examined and the operator is then considered as the generalized Grushin operator. The paramount proofs were Poincar$\acute{e}$ inequality, Gaussian two-bounded estimate for the related heat kernels and the doubling condition for the metric defined by the underlying vector fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19697 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Grushin Operator on Infinite Dimensional Homogeneous Lie Groups Egwe, M. E. Opadara, J. I. Functional Analysis 22Exx, 47Axx, 47Dxx, 32W05 A collection of infinite dimensional complete vector fields $\left\{V_i\right\}_{i=1}^{\infty}$ acting on a locally convex manifolds $M$ on which a smooth positive measure $μ$ is defined was considered. It was assumed that the vector fields generates an infinite dimensional Lie algebra $\mathfrak{g}$ and satisfies H$\ddot{o}$rmander's condition. The sum of squares of Grushin operators related to the vector fields was examined and the operator is then considered as the generalized Grushin operator. The paramount proofs were Poincar$\acute{e}$ inequality, Gaussian two-bounded estimate for the related heat kernels and the doubling condition for the metric defined by the underlying vector fields. |
| title | Grushin Operator on Infinite Dimensional Homogeneous Lie Groups |
| topic | Functional Analysis 22Exx, 47Axx, 47Dxx, 32W05 |
| url | https://arxiv.org/abs/2411.19697 |