BOUNDARY VALUE PROBLEMS OF CONJUGATE AND GENERALIZED $k$-HOLOMORPHIC FUNCTIONS IN $\mathbb{C}^2$*

doi:10.1007/s10473-024-0511-6

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (5): 1837-1852.doi: 10.1007/s10473-024-0511-6

BOUNDARY VALUE PROBLEMS OF CONJUGATE AND GENERALIZED $k$-HOLOMORPHIC FUNCTIONS IN $\mathbb{C}^2$^*

Yanyan CUI¹, Chaojun WANG¹, Yonghong XIE², Yuying QIAO^2,†

1. College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China;
2. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China

收稿日期:2023-02-08 修回日期:2024-05-30 出版日期:2024-10-25 发布日期:2024-10-22
通讯作者: †Yuying QIAO, E-mail,: yuyingqiao@163.com
作者简介:Yanyan CUI,E-mail,: cui9907081@163.com; Chaojun WANG,E-mail,: wang9907081@163.com; Yonghong XIE,E-mail,: xyh1973@126.com
基金资助:
Cui's research was supported by the NSF of Henan Province (222300420397, 242300421394), Xie's research was supported by the NSFC (11571089, 11871191).

BOUNDARY VALUE PROBLEMS OF CONJUGATE AND GENERALIZED $k$-HOLOMORPHIC FUNCTIONS IN $\mathbb{C}^2$^*

Yanyan CUI¹, Chaojun WANG¹, Yonghong XIE², Yuying QIAO^2,†

1. College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China;
2. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China

Received:2023-02-08 Revised:2024-05-30 Online:2024-10-25 Published:2024-10-22
Contact: †Yuying QIAO, E-mail,: yuyingqiao@163.com
About author:Yanyan CUI,E-mail,: cui9907081@163.com; Chaojun WANG,E-mail,: wang9907081@163.com; Yonghong XIE,E-mail,: xyh1973@126.com
Supported by:
Cui's research was supported by the NSF of Henan Province (222300420397, 242300421394), Xie's research was supported by the NSFC (11571089, 11871191).

摘要/Abstract

摘要： In this paper, conjugate $k$-holomorphic functions and generalized $k$-holomorphic functions are defined in the two-dimensional complex space, and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders. By the characteristics of the corresponding functions and boundary properties of the Cauchy type singular integral operators with conjugate $k$-holomorphic kernels, the general solutions and special solutions of the corresponding boundary value problems are studied in a detailed fashion, and the integral expressions of the solutions are obtained.

关键词: several complex variables, $k$-holomorphic functions, partial difference equations, polyanalytic functions

Abstract: In this paper, conjugate $k$-holomorphic functions and generalized $k$-holomorphic functions are defined in the two-dimensional complex space, and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders. By the characteristics of the corresponding functions and boundary properties of the Cauchy type singular integral operators with conjugate $k$-holomorphic kernels, the general solutions and special solutions of the corresponding boundary value problems are studied in a detailed fashion, and the integral expressions of the solutions are obtained.

Key words: several complex variables, $k$-holomorphic functions, partial difference equations, polyanalytic functions

中图分类号:

32A30

Yanyan CUI, Chaojun WANG, Yonghong XIE, Yuying QIAO. BOUNDARY VALUE PROBLEMS OF CONJUGATE AND GENERALIZED $k$-HOLOMORPHIC FUNCTIONS IN $\mathbb{C}^2$^*[J]. 数学物理学报(英文版), 2024, 44(5): 1837-1852.

Yanyan CUI, Chaojun WANG, Yonghong XIE, Yuying QIAO. BOUNDARY VALUE PROBLEMS OF CONJUGATE AND GENERALIZED $k$-HOLOMORPHIC FUNCTIONS IN $\mathbb{C}^2$^*[J]. Acta mathematica scientia,Series B, 2024, 44(5): 1837-1852.

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BOUNDARY VALUE PROBLEMS OF CONJUGATE AND GENERALIZED $k$-HOLOMORPHIC FUNCTIONS IN $\mathbb{C}^2$^*

BOUNDARY VALUE PROBLEMS OF CONJUGATE AND GENERALIZED $k$-HOLOMORPHIC FUNCTIONS IN $\mathbb{C}^2$^*

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