哈代希尔伯特空间上复Volterra算子的数值域  

Numerical Range of the Complex Volterra Operator on Hardy Hilbert Space

作　　者：王攀星 梁玉霞 庞淞月 Wang Panxing;Liang Yuxia;Pang Songyue(School of Mathematical Sciences,Tianjin Normal University,Tianjin 300387)

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《数学物理学报（A辑）》2024年第2期276-285,共10页Acta Mathematica Scientia

基　　金：天津师范大学教学改革项目(JG01223082)。

摘　　要：哈代希尔伯特空间上复Volterra算子数值域的探究一直是数学家们关注的热点课题,却一直未得到解决.该文主要给出了哈代希尔伯特空间上一个权序列为(h,k,j,b,a,b,a,…),其中a,b,h,k,j>0的单边加权移位算子的数值半径计算公式.尤其将该结果应用于求解哈代希尔伯特空间上复Volterra算子的数值域范围.这些研究结果可以有效促进对具有扰动周期权或调和权的加权移位算子数值域的进一步研究,并为哈代希尔伯特空间上有界线性算子数值域的研究提供典型实例.The investigation on the numerical range of the complex Volterra operator on Hardy Hilbert space has always been a hot topic for mathematicians,which has not been solved.In this paper,we present the formulas for the numerical radius of an unilateral weighted shift operator with weights(h,k,j,b,a,b,a,-),where a,b,h,k,j>0.In particular,we apply the above result to calculate the numerical range of the complex Volterra operator on Hardy Hilbert space.These results can not only effectively facilitate further study of the numerical ranges of weighted shift operators with disturbed periodic weights and harmonic weights,but also provide typical examples for the numerical range of bounded linear operators on Hardy Hilbert space.

关 键 词：数值域 数值半径 单边加权移位算子 复Volterra算子 

分 类 号：O177.1[理学—数学]