Uniform bounds of prolate spheroidal wave functions and eigenvalues decay

DOI10.1016/j.crma.2014.01.004zbMath1286.42034arXiv1509.02651OpenAlexW1972102407MaRDI QIDQ2445189

Aline Bonami, Abderrazek Karoui

Publication date: 14 April 2014

Published in: Applied and Computational Harmonic Analysis, Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.02651

zbMATH Keywords

Sobolev spacesspectral approximationprolate spheroidal wave functionseigenvalues and eigenfunctions estimates

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Error bounds for numerical methods for ordinary differential equations (65L70) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15)

Related Items (18)

Generalized prolate spheroidal wave functions: spectral analysis and approximation of almost band-limited functions ⋮ The finite Hankel transform operator: some explicit and local estimates of the eigenfunctions and eigenvalues decay rates ⋮ Reconstruction from the Fourier transform on the ball via prolate spheroidal wave functions ⋮ The approximation of almost time- and band-limited functions by their expansion in some orthogonal polynomials bases ⋮ Spectral decay of time and frequency limiting operator ⋮ Weighted finite Laplace transform operator: spectral analysis and quality of approximation by its eigenfunctions ⋮ Non-asymptotic bounds for discrete prolate spheroidal wave functions analogous with prolate spheroidal wave function bounds ⋮ Computing Fourier integral operators with caustics ⋮ Uniform bounds of prolate spheroidal wave functions and eigenvalues decay ⋮ Hölder-logarithmic stability in Fourier synthesis ⋮ Uniform approximation and explicit estimates for the prolate spheroidal wave functions ⋮ Estimates for the SVD of the truncated Fourier transform on \(L^2(\cosh (B|\cdot |))\) and stable analytic continuation ⋮ Ball prolate spheroidal wave functions in arbitrary dimensions ⋮ Discrete prolate spheroidal wave functions: further spectral analysis and some related applications ⋮ Adaptive estimation in the linear random coefficients model when regressors have limited variation ⋮ Non-asymptotic behavior of the spectrum of the sinc-kernel operator and related applications ⋮ Numerical reconstruction from the Fourier transform on the ball using prolate spheroidal wave functions ⋮ Efficient representation and accurate evaluation of oscillatory integrals and functions

Cites Work

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