Ball prolate spheroidal wave functions in arbitrary dimensions

DOI10.1016/j.acha.2018.08.001zbMath1445.42018arXiv1802.03684OpenAlexW2964328506WikidataQ129418592 ScholiaQ129418592MaRDI QIDQ2300748

Zhimin Zhang, Li-Lian Wang, Jing Zhang, Hui-yuan Li

Publication date: 28 February 2020

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.03684

zbMATH Keywords

finite Fourier transformSturm-Liouville differential equationgeneralized prolate spheroidal wave functionsarbitrary unit ballBouwkamp spectral-algorithm

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Computation of special functions and constants, construction of tables (65D20) Other functions coming from differential, difference and integral equations (33E30) Other special orthogonal polynomials and functions (33C47) Harmonic analysis and PDEs (42B37)

Related Items (6)

Data-Driven Basis for Reconstructing the Contrast in Inverse Scattering: Picard Criterion, Regularity, Regularization, and Stability ⋮ Sampling and approximation of bandlimited volumetric data ⋮ Müntz ball polynomials and Müntz spectral-Galerkin methods for singular eigenvalue problems ⋮ Numerical analysis on the mortar spectral element methods for Schrödinger eigenvalue problem with an inverse square potential ⋮ Gaussian bounds for the heat kernel associated to prolate spheroidal wave functions with applications ⋮ A posteriori error estimates of spectral approximations for second order partial differential equations in spherical geometries

Uses Software

• Algorithm 840

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Slepian spatial-spectral concentration on the ball
• Generalized prolate spheroidal wave functions: spectral analysis and approximation of almost band-limited functions
• On \(hp\)-convergence of prolate spheroidal wave functions and a new well-conditioned prolate-collocation scheme
• Prolate spheroidal wave functions of order zero. Mathematical tools for bandlimited approximation
• Concentration problems for bandpass filters in communication theory over disjoint frequency intervals and numerical solutions
• A new class of highly accurate differentiation schemes based on the prolate spheroidal wave functions
• Optimal spectral schemes based on generalized prolate spheroidal wave functions of order \(-1\)
• Duration and bandwidth limiting. Prolate functions, sampling, and applications.
• A new generalization of the PSWFs with applications to spectral approximations on quasi-uniform grids
• Spectral analysis of the finite Hankel transform and circular prolate spheroidal wave functions
• Approximate formulae for certain prolate spheroidal wave functions valid for large values of both order and band-limit
• Prolate spheroidal wave functions on a disc -- integration and approximation of two-dimensional bandlimited functions
• A generalization of prolate spheroidal functions with more uniform resolution to the triangle
• Large mode number eigenvalues of the prolate spheroidal differential equation.
• High-frequency asymptotic expansions for certain prolate spheroidal wave functions
• On the evaluation of prolate spheroidal wave functions and associated quadrature rules
• Approximation scheme for essentially bandlimited and space-concentrated functions on a disk
• The fast Slepian transform
• New efficient methods of computing the prolate spheroidal wave functions and their corresponding eigenvalues
• Uniform bounds of prolate spheroidal wave functions and eigenvalues decay
• On the calculation of the finite Hankel transform eigenfunctions
• A new friendly method of computing prolate spheroidal wave functions and wavelets
• Prolate spheroidal wavefunctions, quadrature and interpolation
• Spectral Methods
• A Review of Prolate Spheroidal Wave Functions from the Perspective of Spectral Methods
• Slepian functions on the sphere, generalized Gaussian quadrature rule
• Spatiospectral Concentration on a Sphere
• A Fast Algorithm for the Calculation of the Roots of Special Functions
• Efficient Computation of Slepian Functions for Arbitrary Regions on the Sphere
• Approximation Theory and Harmonic Analysis on Spheres and Balls
• Grids and transforms for band-limited functions in a disk
• Algorithm 840: computation of grid points, quadrature weights and derivatives for spectral element methods using prolate spheroidal wave functions---prolate elements
• Spectral Methods Based on Prolate Spheroidal Wave Functions for Hyperbolic PDEs
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - I
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - II
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty-III: The Dimension of the Space of Essentially Time- and Band-Limited Signals
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - IV: Extensions to Many Dimensions; Generalized Prolate Spheroidal Functions
• On Spheroidal Wave Functions of Order Zero

This page was built for publication: Ball prolate spheroidal wave functions in arbitrary dimensions