一类带根号的Riemann边值逆问题在正则情况下的解法  

The solution of a class of inverse Riemann boundary value problems with roots in the case of normal type

作　　者：柏淞玮 孙梦 李平润[1] 王文静 BAI Songwei;SUN Meng;LI Pingrun;WANG Wenjing(School of Mathematical Sciences,Qufu Normal University,273165,Qufu,Shandong,PRC)

机构地区：[1]曲阜师范大学数学科学学院,山东省曲阜市273165

出　　处：《曲阜师范大学学报(自然科学版)》2025年第2期25-30,共6页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金(11971015);山东省大学生创新创业训练计划(S202210446044).

摘　　要：该文研究了在正则型情况下无穷直线上的一类带有根号的Riemann边值逆问题.通过分析未知函数的结构,进行一系列的积分变换,将Riemann边值逆问题转化为经典的全纯函数边值问题.利用解析开拓原理和推广的Liouville定理等,给出了边值问题的一般解.In this paper,a class of inverse Riemann boundary value problems with roots on infinite straight lines in the case of normal type is studied.By using a series of integral transforms,the structure of unknown functions is analyzed and the inverse Riemann boundary value problems is transformed into the classical Riemann boundary value problems.By means of the principle of analytic continuation and the generalized Liouville theorem,the general solution of the equation is obtained.

关 键 词：RIEMANN边值逆问题 解析开拓原理 指标 典则函数 正则型 

分 类 号：O175.5[理学—数学] O175.8[理学—基础数学]