On discrete symplectic systems: Associated maximal and minimal linear relations and nonhomogeneous problems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:421

Article

Clark, Stephen L.¹  Zemanek, Petr² 

[1] Missouri Univ Sci & Technol, Dept Math & Stat, Rolla, MO 65409 USA

[2] Masaryk Univ, Fac Sci, Dept Math & Stat, CZ-61137 Brno, Czech Republic

关键词: Discrete symplectic system;    Time-reversed system;    Definiteness condition;    Nonhomogeneous problem;    Deficiency index;    Linear relation;   

DOI  :  10.1016/j.jmaa.2014.07.015

来源: Elsevier

【 摘 要 】

In this paper we characterize the definiteness of the discrete symplectic system, study a nonhomogeneous discrete symplectic system, and introduce the minimal and maximal linear relations associated with these systems. Fundamental properties of the corresponding deficiency indices, including a relationship between the number of square summable solutions and the dimension of the defect subspace, are also derived. Moreover, a sufficient condition for the existence of a densely defined operator associated with the symplectic system is provided. (c) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free