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

Anirudha Poria*, Ramakrishnan Radha

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 (Formula presented.) 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.

Original languageEnglish
Pages (from-to)1859-1875
Number of pages17
JournalApplicable Analysis
Volume104
Issue number10
DOIs
Publication statusPublished - 29 Nov 2024

Keywords

  • Jacobi–Cherednik operator
  • Markov processes
  • Opdam–Cherednik transform
  • Poisson's equation
  • heat semigroup

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