We introduce a fast algorithm for computing volume potentials - that is, theconvolution of a translation invariant, free-space Green's function with acompactly supported source distribution defined on a uniform grid. Thealgorithm relies on regularizing the Fourier transform of the Green's functionby cutting off the interaction in physical space beyond the domain of interest.This permits the straightforward application of trapezoidal quadrature and thestandard FFT, with superalgebraic convergence for smooth data. Moreover, themethod can be interpreted as employing a Nystrom discretization of thecorresponding integral operator, with matrix entries which can be obtainedexplicitly and rapidly. This is of use in the design of preconditioners or fastdirect solvers for a variety of volume integral equations. The method proposedpermits the computation of any derivative of the potential, at the cost of anadditional FFT.
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