A multidimensional interpolator based on convolution with the sinc function is developed. The interpolator is global in nature, with all sampled data contributing to the computation. Preprocessing of the data by partial summation accelerates convergence of the actual interpolation, when repeatedly interpolating the same data. Modification of the interpolation procedure gives an efficient method for numerical differentiation. The method is intended for bandlimited functions with finite support. The interpolator was tested for a class of problems related to molecular dynamics, including interpolation of 1D, 2D and 3D Gaussian wave packets on a grid; integration of classical trajectories on an interpolated potential; and the transfer of a sampled wave function from a polar grid to a Cartesian grid and back. It was found that the interpolator is very accurate for Gaussian-like wave functions, and that even for functions which are not bandlimited, such as the Morse potential, a reasonable accuracy can be obtained.