On Discrete Symplectic Systems: Associated Maximal and Minimal Linear Relations and Nonhomogeneous Problems
Abstract
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.
Recommended Citation
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
Department(s)
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)
0022-247X
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2015 Elsevier, All rights reserved.
Publication Date
01 Jan 2015
Comments
This work was supported by the Program of “Employment of Newly Graduated Doctors of Science for Scientific Excellence†(grant number CZ.1.07/2.3.00/30.0009 ) co-financed from European Social Fund and the state budget of the Czech Republic.