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黎曼zeta函数之一ks变换献给杨乐先生八十华诞
葛力明
2019
Source Publication数学学报
ISSN0583-1431
Volume62Issue:5Pages:673
Abstract我们定义了KS-变换和自然数乘法结构相关的Fourier变换,建立了实数乘法半群$\left {1,\infty } \right) = \left\{ {x:x \in \mathbb{R},x \ge 1} \right\}$和复半平面$\Omega = \left\{ {s = \sigma + it:\sigma,t \in \mathbb{R},\sigma \ge \frac{1}{2}} \right\}$之间的由KS-变换诱导的对偶关系,证明了KS-变换是希尔伯特空间${L^2}\left( {\left {1,\infty } \right)} \right)$和哈代空间${H^2}\left( \Omega \right)$之间的等距算子,而且该算子保持了相关的函数空间之间由实数的乘法卷积和复数点点相乘诱导出的代数结构的同构.作为应用,我们给出了黎曼假设成立的有关算子指标的等价命题,从而算子理论为研究黎曼$\zeta $-函数和自然数的乘法结构提供了新思路.
Language英语
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/33404
Collection数学所
Affiliation中国科学院数学与系统科学研究院
Recommended Citation
GB/T 7714
葛力明. 黎曼zeta函数之一ks变换献给杨乐先生八十华诞[J]. 数学学报,2019,62(5):673.
APA 葛力明.(2019).黎曼zeta函数之一ks变换献给杨乐先生八十华诞.数学学报,62(5),673.
MLA 葛力明."黎曼zeta函数之一ks变换献给杨乐先生八十华诞".数学学报 62.5(2019):673.
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