On admissibility of the resolvent of discrete Volterra equations

Suppose that a pair of sequence spaces is admissible with respect to a discrete linear Volterra operator. This paper gives sufficient conditions for the same pair of spaces to be admissible with respect to the associated resolvent operator. The spaces considered include spaces of weighted bounded and weighted convergent sequences. Classes of discrete kernels are discussed for which the appropriate weight sequences are not purely exponential, but the product of an exponential and a slowly decaying sequence.