Characterization of Self-Adjoint Extensions for Discrete Symplectic Systems
All self-adjoint extensions of minimal linear relation associated with the discrete symplectic system are characterized. Especially, for the scalar case on a finite discrete interval some equivalent forms and the uniqueness of the given expression are discussed and the Krein-von Neumann extension is described explicitly. In addition, a limit point criterion for symplectic systems is established. The result partially generalizes even the classical limit point criterion for the second order Sturm-Liouville difference equations.
P. Zemanek and S. L. Clark, "Characterization of Self-Adjoint Extensions for Discrete Symplectic Systems," Journal of Mathematical Analysis and Applications, vol. 440, no. 1, pp. 323 - 350, Elsevier, Aug 2016.
The definitive version is available at https://doi.org/10.1016/j.jmaa.2016.03.028
Mathematics and Statistics
Keywords and Phrases
Discrete symplectic system; Krein-von Neumann extension; Limit point criterion; Linear relation; Self-adjoint extension; Uniqueness
International Standard Serial Number (ISSN)
Article - Journal
© 2016 Elsevier, All rights reserved.
01 Aug 2016
This work was supported by the Program of â€œEmployment of Newly Graduated Doctors of Science for Scientific Excellenceâ€ (grant number CZ.1.07/2.3.00/30.0009) co-financed from European Social Fund and the state budget of the Czech Republic.