Prolate spheroidal wave functions provide a natural and effective tool for computing with bandlimited functions defined on an interval. As demonstrated by Slepian et al., the so called generalized prolate spheroidal functions (GPSFs) extend this apparatus to higher dimensions. While the analytical and numerical apparatus in one dimension is fairly complete, the situation in higher dimensions is less satisfactory. This report attempts to improve the situation by providing analytical and numerical tools for GPSFs, including the efficient evaluation of eigenvalues, the construction of quadratures, interpolation formulae, etc. Our results are illustrated with several numerical examples.
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