ABSTRACT
The main result of the paper gives explicit asymptotic formulae for the solutions of the system of higher order linear recurrence equations x ( n + 1 ) = ∑ ι = 0 k [ A i + B i ( n ) ] x ( n − i ) , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203745854/a0661dc5-cfc8-48ab-844c-916895f230b9/content/eq1987.tif"/> where A i and B i (n) are square matrices, provided that the roots of the characteristic equation det ( λ I − ∑ ι = 0 k λ − ι A i ) = 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203745854/a0661dc5-cfc8-48ab-844c-916895f230b9/content/eq1988.tif"/> of the corresponding autonomous equation have distinct moduli and ∑ n = 0 ∞ | B i ( n ) | 2 < ∞ , i = 0 , 1 , … , k . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203745854/a0661dc5-cfc8-48ab-844c-916895f230b9/content/eq1989.tif"/>
