Apparent Singularities of Linear Difference Equations with Polynomial Coefficients
经典分析与常微分方程
2007-05-23 v1
摘要
Let L be a linear difference operator with polynomial coefficients. We consider singularities of L that correspond to roots of the trailing (resp. leading) coefficient of L. We prove that one can effectively construct a left multiple with polynomial coefficients L' of L such that every singularity of L' is a singularity of L that is not apparent. As a consequence, if all singularities of L are apparent, then L has a left multiple whose trailing and leading coefficients equal 1.
引用
@article{arxiv.math/0409508,
title = {Apparent Singularities of Linear Difference Equations with Polynomial Coefficients},
author = {S. A. Abramov and M. A. Barkatou and M. van Hoeij},
journal= {arXiv preprint arXiv:math/0409508},
year = {2007}
}