On discrete symplectic systems: associated maximal and minimal linear relations and nonhomogeneous problems

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Authors

CLARK Stephen L. ZEMÁNEK Petr

Year of publication 2015
Type Article in Periodical
Magazine / Source Journal of Mathematical Analysis and Applications
MU Faculty or unit

Faculty of Science

Citation
Doi http://dx.doi.org/10.1016/j.jmaa.2014.07.015
Field General mathematics
Keywords discrete symplectic system; time-reversed system; definiteness condition; nonhomogeneous problem; Hilbert space; maximal linear relation; minimal linear relation; deficiency index.
Attached files
Description 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.
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