Geodesic
Asymptotic Properties of Convolution Products of Sequences
Publications de l'Institut Mathématique, _N_S_36 (1984) no. 50, p. 67 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Suppose three sequences $\{a_n\}_{\bold N}$, $\{b_n\}_{\boldN}$ and $\{c_n\}_{\bold N}$ are related by the equation $c_n=\sum^n_{k=0}a_{n-k}b_k$. In this paper we examine the asymptotic behavior of $c_n/a_n$ under various conditions on $\{a_n\}_{\bold N}$ and $\{b_n\}_{\bold N}$. If $\sum^\infty_{k=0}|b_k|\infty$ we discuss conditions under which $c_n/a_n\to\sum^n_{k=0}b_k$ and give sharp rate of convergence results. From our results we obtain asymptotic expansions of the form $ c_n = a_n \sum^\infty_{k=0} b_k + (a_n - a_{n-1}) \sum^\infty_{k=1} k b_k + O (|a_n - a_{n-1}|/n). $
Classification : 40A05 40A25 
@article{PIM_1984_N_S_36_50_a9,
     author = {Edward Omey},
     title = {Asymptotic {Properties} of {Convolution} {Products} of {Sequences}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {67 },
     publisher = {mathdoc},
     volume = {_N_S_36},
     number = {50},
     year = {1984},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1984_N_S_36_50_a9/}
}
TY  - JOUR
AU  - Edward Omey
TI  - Asymptotic Properties of Convolution Products of Sequences
JO  - Publications de l'Institut Mathématique
PY  - 1984
SP  - 67 
VL  - _N_S_36
IS  - 50
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PIM_1984_N_S_36_50_a9/
LA  - en
ID  - PIM_1984_N_S_36_50_a9
ER  - 
%0 Journal Article
%A Edward Omey
%T Asymptotic Properties of Convolution Products of Sequences
%J Publications de l'Institut Mathématique
%D 1984
%P 67 
%V _N_S_36
%N 50
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PIM_1984_N_S_36_50_a9/
%G en
%F PIM_1984_N_S_36_50_a9
Edward Omey. Asymptotic Properties of Convolution Products of Sequences. Publications de l'Institut Mathématique, _N_S_36 (1984) no. 50, p. 67 . http://geodesic.mathdoc.fr/item/PIM_1984_N_S_36_50_a9/