Spectral analysis of the finite Hankel transform and circular prolate spheroidal wave functions

DOI10.1016/j.cam.2009.07.037zbMath1180.65170OpenAlexW1983170956MaRDI QIDQ732136

Taher Moumni, Abderrazek Karoui

Publication date: 9 October 2009

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2009.07.037

zbMATH Keywords

numerical resultsJacobi polynomialsBessel functionsquadrature formulaeeigenvalues and eigenfunctionsquadrature formula methodfinite Hankel transformcircular prolate spheroidal wave functions

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Computation of special functions and constants, construction of tables (65D20) Numerical methods for integral transforms (65R10) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Eigenvalue problems for integral equations (45C05) Lamé, Mathieu, and spheroidal wave functions (33E10) Numerical approximation and evaluation of special functions (33F05)

Related Items (12)

On essentially time and Hankel band-limited functions ⋮ Spectrum of the finite Dunkl transform operator and Donoho–Stark uncertainty principle ⋮ Solution of the energy concentration problem and application ⋮ The finite Hankel transform operator: some explicit and local estimates of the eigenfunctions and eigenvalues decay rates ⋮ Asymptotic behaviors and numerical computations of the eigenfunctions and eigenvalues associated with the classical and circular prolate spheroidal wave functions ⋮ Prolate spheroidal wave functions associated with the canonical Fourier–Bessel transform and uncertainty principles ⋮ Unidimensional and bidimensional prolate spheroidal wave functions and applications ⋮ A generalization of the prolate spheroidal wave functions with applications to sampling ⋮ Fourier and Hankel bandlimited signal recovery ⋮ On the calculation of the finite Hankel transform eigenfunctions ⋮ Ball prolate spheroidal wave functions in arbitrary dimensions ⋮ Eigenfunctions of the Airy's integral transform: Properties, numerical computations and asymptotic behaviors

Uses Software

• Maple

Cites Work

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• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - II
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - IV: Extensions to Many Dimensions; Generalized Prolate Spheroidal Functions

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