ℂ2中共轭函数和广义k-荷态函数的边界值问题

IF 1.2 4区数学 Q1 MATHEMATICS

Acta Mathematica Scientia Pub Date : 2024-08-27 DOI:10.1007/s10473-024-0511-6

Yanyan Cui, Chaojun Wang, Yonghong Xie, Yuying Qiao

{"title":"ℂ2中共轭函数和广义k-荷态函数的边界值问题","authors":"Yanyan Cui, Chaojun Wang, Yonghong Xie, Yuying Qiao","doi":"10.1007/s10473-024-0511-6","DOIUrl":null,"url":null,"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.","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":"4 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Boundary value problems of conjugate and generalized k-holomorphic functions in ℂ2\",\"authors\":\"Yanyan Cui, Chaojun Wang, Yonghong Xie, Yuying Qiao\",\"doi\":\"10.1007/s10473-024-0511-6\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":50998,\"journal\":{\"name\":\"Acta Mathematica Scientia\",\"volume\":\"4 1\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-08-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Scientia\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10473-024-0511-6\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Scientia","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10473-024-0511-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文定义了二维复空间中的共轭 k-holomorphic 函数和广义 k-holomorphic 函数，并讨论了广义双轴上相应的黎曼边界值问题和逆问题。通过相应函数的特征和具有共轭 k-holomorphic 核的 Cauchy 型奇异积分算子的边界性质，详细研究了相应边界值问题的通解和特解，并得到了解的积分表达式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Boundary value problems of conjugate and generalized k-holomorphic functions in ℂ2

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Acta Mathematica Scientia 数学-数学

CiteScore

2.00

自引率

10.00%

发文量

2614

审稿时长

6 months

期刊介绍： Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981. The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.