四元数分析中光滑曲面上的 Poincaré-Bertrand 公式

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Poincaré-Bertrand Formula on Smooth Surfaces in Quaternion Analysis

Poincaré-Bertrand Formula on Smooth Surfaces in Quaternion Analysis

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Acta mathematica scientia,Series A ›› 2025, Vol. 45 ›› Issue (2): 534-553.

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Yujie Zhou^1,^*(),Weiyu Luo²(),Yufeng Wang³(),Zhongxiang Zhang³()

¹Faculty of Science and Technology,University of Macau, Macau 999078
²School of Mathematics and Statistics, Guangxi Normal University, Guangxi Guilin 541004
³School of Mathematics and Statistics, Wuhan University, Wuhan 430079

Received:2024-02-16 Revised:2024-09-24 Online:2025-04-26 Published:2025-04-09
Contact: Yujie Zhou E-mail:651397389@qq.com;luoweiyu18@163.com;wh_yfwang@163.com;zhxzhang.math@whu.edu.cn
Supported by:
NSFC(11223344)

Abstract:

Quaternion algebra is an algebraic structure that satisfies the associative law but not the commutative law. It has important theoretical significance and application value for studying equations and operators in high-dimensional spaces. By first proving the Privalov theorem with parameter variables in quaternion analysis, then proving the commutation formula of non principal value products, and finally using mathematical analysis methods to take limits on both sides, the Poincaré-Bertrand formula on smooth surfaces is proved.

Key words: quaternion analysis, Cauchy type singular integral, Poincaré-Bertrand formula

CLC Number:

O175.23

Yujie Zhou,Weiyu Luo,Yufeng Wang,Zhongxiang Zhang. Poincaré-Bertrand Formula on Smooth Surfaces in Quaternion Analysis[J].Acta mathematica scientia,Series A, 2025, 45(2): 534-553.

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[1]	杨丕文. 四元数分析与偏微分方程. 北京: 科学出版社, 2009
	Yang P W. Quaternion Analysis and Partial Differential Equations. Beijing: Science Press, 2009
[2]	Brack F, Delanghe R, Sommen F. Clifford Analysis. Boston: Pitman Books Limits, 1982
[3]	路见可. 解析函数边值问题. 武汉: 武汉大学出版社, 2004
	Lu J K. Analytical Function Boundary Value Problems. Wuhan: Wuhan University, 2004
[4]	Kandmanov R M. Bochner-Martinelli integrals and their applications. Sciences Siberia Press, 1992, 100: 209-213
[5]	黄沙. Clifford 分析中奇异积分方程的 Poincaré-Bertrand 公式. 数学学报, 1998, 41(1) : 119-126 doi: 10.12386/A1998sxxb0045
	Huang S. Poincaré-Bertrand transformation formulae of the singular integrals in Clifford analysis. Acta Mathematica Sinica, 1998, 41(1): 119-126 doi: 10.12386/A1998sxxb0045
[6]	罗纬宇. Clifford 分析中正则函数边值问题及奇异积分方程. 武汉: 武汉大学出版社, 2014
	Luo W Y. The regularization function boundary value problem and singular integral equation in Clifford analysis. Wuhan: Wuhan University, 2014
[7]	Huang S, Qiao Y Y, Wen G C. Real and Complex Clifford Analysis. New York: Springer, 2006
[8]	Xu Q H, Ma T, Yin Z. Functional Analysis. Beijing: Higher Education Press, 2017
[9]	Gilbert R P, Buchanan J L. First order elliptic systems, a function theoretic approach. Mathematics in Science Engineering, 1983, 163: Art 281
[10]	Rankin R A. Real and Complex Analysis. By W. Rudin. Pp. 412. 84s. 1966. (McGraw-Hill, New York.). The Mathematical Gazette, 1968, 52(382): 412
[11]	Luo W Y, Du J. Generalized Cauchy theorem in Clifford analysis and boundary value problems for regular functions. Advances in Applied Clifford Algebras, 2017, 27: 2531-2583
[12]	Zhang Z X, Du J Y. On certain Riemann boundary value problems and singular integral equations in Clifford analysis. Chinese Journal of Contemporary Mathematics, 2001, 22(3): 237-244
[13]	Du J Y, Zhang Z X. A Cauchy's integral formula for functions with values in a universal Clifford algebral and its applications. Complex Variables, 2002, 47(10): 915-928
[14]	Du J Y, Xu N, Zhang Z X. Boundary behavior of Cauchy-type integrals in Clifford analysis. Acta Math Sci, 2009, 29(1): 210-224

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