杨向东,曾毕君.关于薛定谔算子的极点散射: 基于狄利克雷级数的视角[J].数学研究及应用,2019,39(2):160~170
关于薛定谔算子的极点散射: 基于狄利克雷级数的视角
On Scattering of Poles for Schr\"{o}dinger Operator from the Point of View of Dirichlet Series
投稿时间:2018-03-30  修订日期:2018-06-05
DOI:10.3770/j.issn:2095-2651.2019.02.005
中文关键词:  共振  薛定谔算子  狄利克雷级数
英文关键词:Resonances  Schr\"{o}dinger operators  Dirichlet series
基金项目:国家自然科学基金(Grant No.11261024).
作者单位
杨向东 昆明理工大学数学系, 云南 昆明 650093 
曾毕君 昆明理工大学数学系, 云南 昆明 650093 
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中文摘要:
      本文讨论了在实轴上具有紧支集的势的薛定谔算子的极点散射问题. 本文旨在将狄利克雷级数理论与散射理论相结合, 文中运用了Littlewood的经典方法得到关于极点个数的新的估计. 本文首次将狄利克雷级数方法用于极点估计, 由此得到了极点个数的上界与下界, 这些结果改进和推广了该论题的一些相关结论.
英文摘要:
      In this article, we are concerned with the scattering problem of Schr\"{o}dinger operators with compactly supported potentials on the real line. We aim at combining the theory of Dirichlet series with scattering theory. New estimate on the number of poles is obtained under the situation that the growth of power series which is related to the potential is not too fast by using a classical result of Littlewood. We propose a new approach of Dirichlet series such that significant upper bounds and lower bounds on the number of poles are obtained. The results obtained in this paper improve and extend some related conclusions on this topic.
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