On Scattering of Poles for Schr\"{o}dinger Operator from the Point of View of Dirichlet Series
Received:March 30, 2018  Revised:June 05, 2018
Key Word: Resonances   Schr\"{o}dinger operators   Dirichlet series  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11261024).
Author NameAffiliation
Xiangdong YANG Department of Mathematics, Kunming University of Science and Technology, Yunnan 650093, P. R. China 
Bijun ZENG Department of Mathematics, Kunming University of Science and Technology, Yunnan 650093, P. R. China 
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Abstract:
      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.
Citation:
DOI:10.3770/j.issn:2095-2651.2019.02.005
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