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@article{984790,
author = {Šimon Hilscher, Roman},
article_number = {12},
doi = {http://dx.doi.org/10.1016/j.laa.2012.06.033},
keywords = {Discrete symplectic system; Oscillation theorem; Finite eigenvalue; Finite eigenfunction; Linear Hamiltonian system; Quadratic functional},
language = {eng},
issn = {0024-3795},
journal = {Linear Algebra and Its Applications},
title = {Oscillation theorems for discrete symplectic systems with nonlinear dependence in spectral parameter},
volume = {437},
year = {2012}
}
TY - JOUR
ID - 984790
AU - Šimon Hilscher, Roman
PY - 2012
TI - Oscillation theorems for discrete symplectic systems with nonlinear dependence in spectral parameter
JF - Linear Algebra and Its Applications
VL - 437
IS - 12
SP - 2922-2960
EP - 2922-2960
PB - Elsevier
SN - 00243795
KW - Discrete symplectic system
KW - Oscillation theorem
KW - Finite eigenvalue
KW - Finite eigenfunction
KW - Linear Hamiltonian system
KW - Quadratic functional
N2 - In this paper we open a new direction in the study of discrete symplectic systems and Sturm-Liouville difference equations by introducing nonlinear dependence in the spectral parameter. We develop the notions of (finite) eigenvalues and (finite) eigenfunctions and their multiplicities, and prove the corresponding oscillation theorem for Dirichlet boundary conditions. The present theory generalizes several known results for discrete symplectic systems which depend linearly on the spectral parameter. Our results are new even for special discrete symplectic systems, namely for Sturm-Liouville difference equations, symmetric three-term recurrence equations, and linear Hamiltonian difference systems.
ER -
ŠIMON HILSCHER, Roman. Oscillation theorems for discrete symplectic systems with nonlinear dependence in spectral parameter. \textit{Linear Algebra and Its Applications}. Elsevier, 2012, vol.~437, No~12, p.~2922-2960. ISSN~0024-3795. doi:10.1016/j.laa.2012.06.033.
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