BOUNDARY VALUE PROBLEMS OF CONJUGATE AND GENERALIZED K-HOLOMORPHIC FUNCTIONS IN C^(2)  

作　　者：Yanyan CUI Chaojun WANG Yonghong XIE Yuying QIAO 崔艳艳;王朝君;谢永红;乔玉英(College of Mathematics and Statistics,Zhoukou Normal University,Zhoukou,466001,China;College of Mathematics and Information Science,Hebei Normal University,Shijiazhuang,050024,China)

机构地区：[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

出　　处：《Acta Mathematica Scientia》2024年第5期1837-1852,共16页数学物理学报（B辑英文版）

基　　金：supported by the NSF of Henan Province(222300420397,242300421394);Xie’s research was supported by the NSFC(11571089,11871191).

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 

分 类 号：O174.52[理学—数学]