  We present a fast, adaptive multiresolution algorithm for applying integral
operators with a wide class of radially symmetric kernels in dimensions one,
two and three. This algorithm is made efficient by the use of separated
representations of the kernel. We discuss operators of the class
$(-\Delta+\mu^{2}I)^{-\alpha}$, where $\mu\geq0$ and $0<\alpha<3/2$, and
illustrate the algorithm for the Poisson and Schr\"{o}dinger equations in
dimension three. The same algorithm may be used for all operators with radially
symmetric kernels approximated as a weighted sum of Gaussians, making it
applicable across multiple fields by reusing a single implementation.
  This fast algorithm provides controllable accuracy at a reasonable cost,
comparable to that of the Fast Multipole Method (FMM). It differs from the FMM
by the type of approximation used to represent kernels and has an advantage of
being easily extendable to higher dimensions.
