引用本文: 张建元1, 韩艳1, 张毅敏1, 赵书芬1, 刘承萍1, 张昕2.无穷直线上K-解析函数的 Riemann 边值问题与 Hilbert 边值问题[J].西南大学学报（自然科学版）,2017,39(8):57~64
【打印本页】   【HTML】   【下载PDF全文】   查看/发表评论  【EndNote】   【RefMan】   【BibTex】
 ←前一篇|后一篇→ 过刊浏览    高级检索
 本文已被：浏览 104次   下载 74次 码上扫一扫！ 分享到： 微信 更多 字体:加大+|默认|缩小- 无穷直线上K-解析函数的 Riemann 边值问题与 Hilbert 边值问题 张建元1, 韩艳1, 张毅敏1, 赵书芬1, 刘承萍1, 张昕2
 作者 单位 张建元1, 韩艳1, 张毅敏1, 赵书芬1, 刘承萍1, 张昕2 1. 昭通学院 数学与统计学院，云南 昭通 657000; 2. 昭通市统计局，云南 昭通 657000

DOI：10.13718/j.cnki.xdzk.2017.08.008

Riemann Boundary Value Problem and Hilbert Boundary Value Problem for K-Analytic Function on an Infinite Straight Line
ZHANG Jian-yuan1, HAN Yan1, ZHANG Yi-min1, ZHAO Shu-fen1, LIU Cheng-ping1, ZHANG xin2
Abstract:
In this paper, we first introduce the concept of K-analytic function of Cauchy type K-integral on an infinite straight line (fragmentation) and use the K-symmetry transformation method to study some properties of the Cauchy type K-integral. Then, with the help of the index that functions on the infinite straight line and the properties of the Cauchy type K-integral, we obtain the solvable conditions and its expression of Riemann boundary value problem of the K-analytic function on the infinite straight line as well as the relationship between them and the index. Finally, we use the K-symmetry expansion function in a half plane to transform the Hilbert boundary value problem into Riemann boundary value problems on the infinite straight line X, thus obtaining the solvable conditions and its expression of the Hilbert boundary value problem. Both the analytic function and the conjugate analytic function are special cases of the K-analytic function. The results obtained in this paper generalize the analytic function and the conjugate analytic function in the corresponding conclusions.
Key words: