%0 Journal Article
%T 正则树上满足&delta;'-型条件的Schr&#214;dinger算子的谱与正交多项式<br>The Spectrum of Schr&#214;dinger Operators with &delta;'-Type Conditions on Regular Trees and Orthogonal Polynomial
%A 宋红梅
%J Advances in Applied Mathematics
%P 1351-1360
%@ 2324-8009
%D 2023
%I Hans Publishing
%R 10.12677/AAM.2023.123137
%X 本文研究了定义在正则度量树Γ<sub>n</sub>上满足δ'-型顶点条件的Schr？dinger算子的谱结构。文章首先给出了正则量子树分解后得到的量子线图上的算子所满足的顶点条件与正交多项式的关系，然后根据L<sub>2</sub>(Γn)的空间分解定理和正交多项式根的性质得到了<span>Γ</span><sub>n</sub>上算子的谱结构。<br />
In this paper, we study the spectral structure of Schr？dinger operators with <span>δ'</span>-type vertex condi-tions on regular metric trees. We first give the relationship between the operators with <span>δ'</span>-type vertex conditions on the quantum graph after the decomposition of the regular quantum tree and the orthogonal polynomials; then we get the spectral structure of Schr？dinger operators on regular metric trees by the space decomposition theorem and the roots’ properties of orthogonal polynomi-als.
%K 正则度量树，顶点条件，正交多项式，谱结构<br>Regular Metric Tree
%K Vertex Condition
%K Orthogonal Polynomials
%K Spectral Structure
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=63461