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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.05376 |
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| _version_ | 1866929673174253568 |
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| author | Poria, Anirudha Radha, Ramakrishnan |
| author_facet | Poria, Anirudha Radha, Ramakrishnan |
| contents | In this paper, we study the heat equation associated with the Jacobi--Cherednik operator on the real line. We establish some basic properties of the Jacobi--Cherednik heat kernel and heat semigroup. We also provide a solution to the Cauchy problem for the Jacobi--Cherednik heat operator and prove that the heat kernel is strictly positive. Then, we characterize the image of the space $L^2(\mathbb R, A_{α, β})$ under the Jacobi--Cherednik heat semigroup as a reproducing kernel Hilbert space. As an application, we solve the modified Poisson equation and present the Jacobi--Cherednik--Markov processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05376 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The heat semigroup associated with the Jacobi--Cherednik operator and its applications Poria, Anirudha Radha, Ramakrishnan Functional Analysis Primary 42A99, Secondary 58J35, 47D07 In this paper, we study the heat equation associated with the Jacobi--Cherednik operator on the real line. We establish some basic properties of the Jacobi--Cherednik heat kernel and heat semigroup. We also provide a solution to the Cauchy problem for the Jacobi--Cherednik heat operator and prove that the heat kernel is strictly positive. Then, we characterize the image of the space $L^2(\mathbb R, A_{α, β})$ under the Jacobi--Cherednik heat semigroup as a reproducing kernel Hilbert space. As an application, we solve the modified Poisson equation and present the Jacobi--Cherednik--Markov processes. |
| title | The heat semigroup associated with the Jacobi--Cherednik operator and its applications |
| topic | Functional Analysis Primary 42A99, Secondary 58J35, 47D07 |
| url | https://arxiv.org/abs/2409.05376 |