Regular approximation of linear Hamiltonian operators with two singular endpoints

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:484

Article

Zhang, Maozhu¹  Li, Kun²  Wang, Yicao³ 

[1] Taishan Univ, Coll Math & Stat, Tai An, Shandong, Peoples R China

[2] Qufu Normal Univ, Sch Math Sci, Qufu, Shandong, Peoples R China

[3] Hohai Univ, Dept Math, Nanjing, Peoples R China

关键词: Regular approximation;    Hamiltonian operators;    Spectral included;   

DOI  :  10.1016/j.jmaa.2019.123758

来源: Elsevier

【 摘 要 】

In this paper we investigate regular approximation of linear Hamiltonian operators with two singular endpoints. For any given singular self-adjoint Hamiltonian operator, its spectrum can be approximated with the eigenvalues of a sequence of regular operators. The inherited restriction operators are constructed by the limit-circle solutions and the limit-point solutions, and proved to be self-adjoint. Via the abstract operator theory, we obtain the strongly resolvent convergence of the inherited regular operators and spectral inclusion of spectrum. Moreover for the case with both endpoints being limit circle, spectral exactness of spectrum is obtained by Hilbert-Schmidt norm convergence. In the case of Friedrichs extension of singular Hamiltonian systems, spectral exactness also holds due to variational principle of eigenvalues. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free