  We introduce a fast algorithm for computing volume potentials - that is, the
convolution of a translation invariant, free-space Green's function with a
compactly supported source distribution defined on a uniform grid. The
algorithm relies on regularizing the Fourier transform of the Green's function
by cutting off the interaction in physical space beyond the domain of interest.
This permits the straightforward application of trapezoidal quadrature and the
standard FFT, with superalgebraic convergence for smooth data. Moreover, the
method can be interpreted as employing a Nystrom discretization of the
corresponding integral operator, with matrix entries which can be obtained
explicitly and rapidly. This is of use in the design of preconditioners or fast
direct solvers for a variety of volume integral equations. The method proposed
permits the computation of any derivative of the potential, at the cost of an
additional FFT.
