Friedrichs extensions for a class of singular discrete linear Hamiltonian systems

2023/11/15 by Guojing Ren, Ren, Guojing, Guixin Xu +1
Computer Science · Mathematics · #FOS: Mathematics #Matrix Theory and Algorithms #Numerical methods for differential equations #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2311.08665

openalex publication_date 2023/11/15 · openalex created_date 2023/11/17 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the characterizations of the Friedrichs extension for a class of singular discrete linear Hamiltonian systems. The existence of recessive solutions and the existence of the Friedrichs extension are proved under some conditions. The self-adjoint boundary conditions are obtained by applying the recessive solutions and then the characterization of the Friedrichs extension is obtained in terms of boundary conditions via linear independently recessive solutions.

Related

• The Friedrichs extension of a class of discrete symplectic systems
• Quasi self-adjoint extensions of a class of formally non-self-adjoint discrete Hamiltonian systems
• Friedrichs systems on an interval
• Generalization of the Hamilton-Jacobi approach for higher order singular systems
• Linear Hamilton Systems without Regular Properties. Solving a Problem Stated by M.G. Krein