The resolvent structure of a Volterra equation with nonsummable difference kernel

In this paper we study the asymptotic behavior of the resolvent of a linear integral Volterra equation whose difference kernel is nonsummable. For a certain class of such kernels the equation is reducible to an equation whose difference kernel is summable. This enables one to use the well-known results on the structure of resolvents of summable kernels in the case of a nonsummable kernel. We apply the obtained results to homogeneous kernels of degree $-1$.