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
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