Title

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.

Department(s)

Mathematics and Statistics

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.

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.

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