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<p>In this paper, the two-sided quaternionic Dunkl transform satisfies some uncertainty principles of quaternion algebra. An analog of the Beurling theorem for the two-sided quaternionic Dunkl transform is obtained. As a direct consequence of Beurling’s theorem, other versions of the uncertainty principle, such as Hardy’s, Gelfand–Shilov’s, Cowling–Price’s and Morgan’s theorems are also deduced.</p>

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The Beurling Theorem for the Two-Sided Quaternionic Dunkl Transform

  • 期刊论文

  • 发表日期：

    2025年10月6日

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  • Othman Tyr

摘要

In this paper, the two-sided quaternionic Dunkl transform satisfies some uncertainty principles of quaternion algebra. An analog of the Beurling theorem for the two-sided quaternionic Dunkl transform is obtained. As a direct consequence of Beurling’s theorem, other versions of the uncertainty principle, such as Hardy’s, Gelfand–Shilov’s, Cowling–Price’s and Morgan’s theorems are also deduced.