@article{Miyazaki2023, 
author = {Rinko Miyazaki and Dohan Kim and Jong Son Shin},
title = {Uniform boundedness of solutions to linear difference equations with periodic forcing functions},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {10},
pages = {24116-24131},
keywords = {uniform boundedness, spectral decomposition, periodic forcing functions, linear difference equation, characteristic equation},
url = {https://www.sciopen.com/article/10.3934/math.20231229},
doi = {10.3934/math.20231229},
abstract = {In this paper we give criteria on the uniform boundedness of the solutions to linear difference equations (LEs) with periodic forcing functions. First, we give a necessary and sufficient condition that the sequence    {      L    n    } of a square matrix    L is bounded, from which a criterion on the uniform boundedness of the solutions to LEs is obtained. Second, a criterion on the uniform boundedness of the solutions for LEs with periodic forcing functions is given by applying a certain representation of solutions. In connection with LEs with delay, we give the characteristic equation of a matrix under the commuting condition.}
}