  The Volterra calculus is a simple and powerful pseudodifferential tool for
inverting parabolic equations and it has also found many applications in
geometric analysis. On the other hand, an important property in the theory of
pseudodifferential operators is the asymptotic completeness, which allows us to
construct parametrices modulo smoothing operators. In this paper we present new
and fairly elementary proofs the asymptotic completeness of the Volterra
calculus.
