Hilbert Boundary Value Problems for Monogenic Functions on the Hyperplane

IF 1.2 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2025-10-03 DOI:10.1007/s00006-025-01411-9

Pei Dang, Jinyuan Du, Tao Qian

引用次数: 0

Abstract

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.

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超平面上单基因函数的Hilbert边值问题

本文系统地研究了超平面上任意整数阶单基因函数无穷远处解的Hilbert边值问题，其中负阶情况即使限制在复平面上下文中也是新的。给出了显式求解公式，并给出了可解条件。利用Clifford对称扩展方法证明了结果，该方法将Hilbert边值问题简化为Riemann边值问题，涉及许多创新的几何技术。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

期刊介绍： Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.