Quasi self-adjoint extensions of a class of formally non-self-adjoint discrete Hamiltonian systems

2025/12/10 by Ren, Guojing, Xu, Guixin
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2512.09594

Abstract

This paper is concerned with the characterizations of quasi self-adjoint extensions of a class of formally non-self-adjoint discrete Hamiltonian systems. Some properties of the solutions and the characterization of the minimal linear relations of the non-self-adjoint systems are obtained. A bijective projection between all the quasi self-adjoint extensions of non-self-adjoint systems and all the self-adjoint extensions of the self-adjoint systems generated by the non-self-adjoint Hamiltonian systems is established in the general case. When the system is in the limit point case and \I=[a,∞), a complete characterization of all the quasi self-adjoint extensions is obtained by a subspace Q⊂ \C²ⁿ with dim Q=n in terms of boundary conditions.

Citations

• Quasi-selfadjoint extensions of dual pairs of linear relations
• Weyl Solutions and J-selfadjointness for Dirac operators
• J-Self-Adjointness of a Class of Dirac-Type Operators
• Weyl-Titchmarsh M-Function Asymptotics, Local Uniqueness Results, Trace Formulas, and Borg-type Theorems for Dirac Operators

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