Discrete Symplectic Systems, Boundary Triplets, and Self-Adjoint Extensions

Abstract

An explicit characterization of all self-adjoint extensions of the minimal linear relation associated with a discrete symplectic system is provided using the theory of boundary triplets with special attention paid to the quasiregular and limit point cases. A particular example of the system (the second order Sturm-Liouville difference equation) is also investigated thoroughly, while higher order equations or linear Hamiltonian difference systems are discussed briefly. Moreover, the corresponding gamma field and Weyl relations are established and their connection with the Weyl solution and the classical M(λ)-function is discussed. To make the paper reasonably self-contained, an extensive introduction to the theory of linear relations, self-adjoint extensions, and boundary triplets is included.

Department(s)

Mathematics and Statistics

Comments

This work was supported by the Grantová Agentura České Republiky, Grant GA19-01246S.

Keywords and Phrases

Boundary Triplets; Discrete Symplectic System; Linear Relation; Self-Adjoint Extension

International Standard Serial Number (ISSN)

1730-6310; 0012-3862

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2022, All rights reserved.

Publication Date

01 Jan 2022

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