On Discrete Symplectic Systems: Associated Maximal and Minimal Linear Relations and Nonhomogeneous Problems
In this paper we characterize the definiteness of the discrete symplectic system, study a nonhomogeneous discrete symplectic system, and introduce the minimal and maximal linear relations associated with these systems. Fundamental properties of the corresponding deficiency indices, including a relationship between the number of square summable solutions and the dimension of the defect subspace, are also derived. Moreover, a sufficient condition for the existence of a densely defined operator associated with the symplectic system is provided.
S. L. Clark and P. Zemanek, "On Discrete Symplectic Systems: Associated Maximal and Minimal Linear Relations and Nonhomogeneous Problems," Journal of Mathematical Analysis and Applications, vol. 421, no. 1, pp. 779-805, Elsevier, Jan 2015.
The definitive version is available at https://doi.org/10.1016/j.jmaa.2014.07.015
Mathematics and Statistics
Keywords and Phrases
Deficiency index; Definiteness condition; Discrete symplectic system; Linear relation; Nonhomogeneous problem; Time-reversed system
International Standard Serial Number (ISSN)
Article - Journal
© 2015 Elsevier, All rights reserved.