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arXiv · 2409.05376

The heat semigroup associated with the Jacobi--Cherednik operator and its applications

Anirudha Poria·Ramakrishnan Radha
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Abstract

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 $L^2(\mathbb R, A_{\alpha, \beta})$ 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.

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Anirudha Poria, Ramakrishnan Radha. 2024-09-09. The heat semigroup associated with the Jacobi--Cherednik operator and its applications. https://doi.org/10.1080/00036811.2024.2434867

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