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The aim of this paper is to give an extension to a Favard classes for integral resolvent of a scalar Volterra integral equations similar to the one for semigroups and resolvent families (i.e., k-regularized resolvent family with ). In fact, we recover several well-known results for semigroups if we consider  and for resolvent families if we consider  arbitrary and  

semigroups, Volterra integral equations, integral resolvent, resolvent family, k-regularized resolvent family, Favard spaces.