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<p>This paper systematically studies Hilbert boundary value problems for monogenic functions on the hyperplane for the solutions being of any integer orders at infinity, where the negative order cases are new even when restricted to the complex plane context. The explicit solution formulas are provided and the solvability conditions are specified. The results are proved using the Clifford symmetric extension method, which reduces Hilbert boundary value problems to Riemann boundary value problems, involving many innovative geometric techniques.</p>

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Hilbert Boundary Value Problems for Monogenic Functions on the Hyperplane

  • 期刊论文

  • 发表日期：

    2025年10月3日

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  • Pei Dang,
  • Jinyuan Du,
  • Tao Qian

摘要

This paper systematically studies Hilbert boundary value problems for monogenic functions on the hyperplane for the solutions being of any integer orders at infinity, where the negative order cases are new even when restricted to the complex plane context. The explicit solution formulas are provided and the solvability conditions are specified. The results are proved using the Clifford symmetric extension method, which reduces Hilbert boundary value problems to Riemann boundary value problems, involving many innovative geometric techniques.