Discrete symplectic systems, boundary triplets, and self-adjoint extensions

Investor logo

Warning

This publication doesn't include Faculty of Economics and Administration. It includes Faculty of Science. Official publication website can be found on muni.cz.
Authors

ZEMÁNEK Petr CLARK Stephen L.

Year of publication 2022
Type Article in Periodical
Magazine / Source Dissertationes Mathematicae
MU Faculty or unit

Faculty of Science

Citation
Web https://www.impan.pl/en/publishing-house/journals-and-series/dissertationes-mathematicae/online/114677/discrete-symplectic-systems-boundary-triplets-and-self-adjoint-extensions
Doi http://dx.doi.org/10.4064/dm838-12-2021
Keywords discrete symplectic system; linear relation; self-adjoint extension; boundary triplets
Description 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(?)-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.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.