CAUCHY INTEGRAL FORMULA FOR K-MONOGENIC FUNCTION WITH $\alpha$-WEIGHT IN SUPERSPACE

doi:10.1007/s10473-025-0305-5

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (3): 825-836.doi: 10.1007/s10473-025-0305-5

CAUCHY INTEGRAL FORMULA FOR K-MONOGENIC FUNCTION WITH $\alpha$-WEIGHT IN SUPERSPACE

Zhiyuan FU¹, Heju YANG^2,†, Na XU³

1. School of Science, Beijing Technology and Business University, Beijing 100048, China; Hebei University of Science and Technology, Shijiazhuang 050018, China;
2. School of Science, Hebei University of Science and Technology, Shijiazhuang 050018, China;
3. School of Economics and Management, Hebei University of Science and Technology, Shijiazhuang 050018, China

收稿日期:2024-02-01 修回日期:2024-04-02 出版日期:2025-05-25 发布日期:2025-09-30

CAUCHY INTEGRAL FORMULA FOR K-MONOGENIC FUNCTION WITH $\alpha$-WEIGHT IN SUPERSPACE

Zhiyuan FU¹, Heju YANG^2,†, Na XU³

1. School of Science, Beijing Technology and Business University, Beijing 100048, China; Hebei University of Science and Technology, Shijiazhuang 050018, China;
2. School of Science, Hebei University of Science and Technology, Shijiazhuang 050018, China;
3. School of Economics and Management, Hebei University of Science and Technology, Shijiazhuang 050018, China

Received:2024-02-01 Revised:2024-04-02 Online:2025-05-25 Published:2025-09-30
Contact: ^†Heju YANG, E-mail: HBKJDX2022@163.com
About author:Zhiyuan FU, E-mail: 435010980@qq.com; Na XU, E-mail: xunaandxuwei123@163.com
Supported by:
National Science Foundation of China (11571089, 11871191) , the National Science Foundation of Hebei (A2022208007, A2024208005), the Hebei University of Science and Technology Dr. Fund (1181348) and the Hebei Normal University Dr. Fund (L2018201).

摘要/Abstract

摘要： Firstly, the definition of $k$-monogenic function with $\alpha$-weight in superspace is given and a series of properties of this function are discussed. Then the Cauchy-Pompeiu formula for $k$-monogenic function with $\alpha$-weight is obtained. Lastly, the Cauchy integral theorem for $k$-monogenic function with $\alpha$-weight is proved.

关键词: Cauchy integral, $k$-monogenic with $\alpha$-weight, superspace

Abstract: Firstly, the definition of $k$-monogenic function with $\alpha$-weight in superspace is given and a series of properties of this function are discussed. Then the Cauchy-Pompeiu formula for $k$-monogenic function with $\alpha$-weight is obtained. Lastly, the Cauchy integral theorem for $k$-monogenic function with $\alpha$-weight is proved.

Key words: Cauchy integral, $k$-monogenic with $\alpha$-weight, superspace

中图分类号:

30E20

Zhiyuan FU, Heju YANG, Na XU. CAUCHY INTEGRAL FORMULA FOR K-MONOGENIC FUNCTION WITH $\alpha$-WEIGHT IN SUPERSPACE[J]. 数学物理学报(英文版), 2025, 45(3): 825-836.

Zhiyuan FU, Heju YANG, Na XU. CAUCHY INTEGRAL FORMULA FOR K-MONOGENIC FUNCTION WITH $\alpha$-WEIGHT IN SUPERSPACE[J]. Acta mathematica scientia,Series B, 2025, 45(3): 825-836.

CAUCHY INTEGRAL FORMULA FOR K-MONOGENIC FUNCTION WITH $\alpha$-WEIGHT IN SUPERSPACE

CAUCHY INTEGRAL FORMULA FOR K-MONOGENIC FUNCTION WITH $\alpha$-WEIGHT IN SUPERSPACE

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