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Numerical Algorithms for the Computation of Generalized Prolate Spheroidal Functions

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arxiv 1710.02874 v1 pith:GS6E7CE7 submitted 2017-10-08 math.NA cs.NA

Roy R. Lederman This is my paper · ORCID
classification math.NAcs.NA
keywords domainfunctionsgeneralizedgpsfsprolatespheroidalaccompaniedalgorithms
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Generalized Prolate Spheroidal Functions (GPSF) are the eigenfunctions of the truncated Fourier transform, restricted to D-dimensional balls in the spatial domain and frequency domain. Despite their useful properties in many applications, GPSFs are often replaced by crude approximations. The purpose of this paper is to review the elements of computing GPSFs and associated eigenvalues. This paper is accompanied by open-source code.

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  1. Eigenvalue distribution analysis of multidimensional prolate matrices

    math.CA 2025-07 conditional novelty 5.0 of 10

    For d-dimensional Cartesian discrete prolate matrices, the number of eigenvalues above a threshold ε is approximately (2MW)^d with an explicit error bound B_d(MW, ε).

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