The paper discusses some known asymptotic stability conditionsfor the difference equation$$x_n = \alpha x_{n -1} + \beta x_{n−k}, n = 0, 1, 2, . . .$$with complex numbers $\alpha$, $\beta$ . As the main result, we show that the system of necessary and sufficient stability conditions, derived in a previous work, can be significantly simplified.
@article{337,
title = {On a three term linear difference equation with complex coefficients},
journal = {Tatra Mountains Mathematical Publications},
volume = {62},
year = {2015},
doi = {10.2478/tatra.v63i0.337},
language = {EN},
url = {http://dml.mathdoc.fr/item/337}
}
Jánský, Jiří. On a three term linear difference equation with complex coefficients. Tatra Mountains Mathematical Publications, Tome 62 (2015) . doi : 10.2478/tatra.v63i0.337. http://gdmltest.u-ga.fr/item/337/