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We provide an explicit description of the weighted Dirichlet space of slice hyperholomorphic functions on the punctured quaternionic open unit ball. We give the explicit formula for its reproducing kernel function as well as its associated integral transform of Bargmann type.

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On the Modified Hyperholomorphic Dirichlet Space on the Punctured Unit Ball

  • 会议论文

  • 发表日期：

    2026年

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  • Sofia Boudrai,
  • Allal Ghanmi,
  • Taoufik Khalil

摘要

We provide an explicit description of the weighted Dirichlet space of slice hyperholomorphic functions on the punctured quaternionic open unit ball. We give the explicit formula for its reproducing kernel function as well as its associated integral transform of Bargmann type.