The structure of the resolvent for the discrete renewal equation with nonsummable difference kernel (Q465105)

For the discrete renewal equation \[ \displaystyle{x_n = \sum_0^na_{n-k}x_k + f_n\;,\;n=0,1,2,\ldots}, \] the authors study the asymptotics of the kernel sequence \(\{a_n\}_n\), when this sequence is not in \(l^1\). Complex domain arguments are used.