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<p>In this paper, we extend fundamental uncertainty principles for the two-sided quaternionic Dunkl transform, including Heisenberg’s inequality and Miyachi’s theorem. From Miyachi’s theorem, we derive further uncertainty principles, such as Hardy’s theorem and the Cowling–Price theorem. Additionally, as an application, we establish an extended form of Heisenberg’s inequality for the general double-sided OPS-QFT.</p>

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Uncertainty principles for the two-sided quaternionic Dunkl transform

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • Mohamed Essenhajy,
  • Said Fahlaoui

摘要

In this paper, we extend fundamental uncertainty principles for the two-sided quaternionic Dunkl transform, including Heisenberg’s inequality and Miyachi’s theorem. From Miyachi’s theorem, we derive further uncertainty principles, such as Hardy’s theorem and the Cowling–Price theorem. Additionally, as an application, we establish an extended form of Heisenberg’s inequality for the general double-sided OPS-QFT.