  Instead of sampling a function at a single point, average sampling takes the
weighted sum of function values around the point. Such a sampling strategy is
more practical and more stable. In this note, we present an explicit method
with an exponentially-decaying approximation error to reconstruct a
multivariate bandlimited function from its finite average oversampling data.
The key problem in our analysis is how to extend a function so that its Fourier
transform decays at an optimal rate to zero at infinity.
