Non-asymptotic behavior and the distribution of the spectrum of the finite Hankel transform operator

DOI10.1080/10652469.2021.1875460zbMath1479.42072arXiv2002.00170OpenAlexW3130680437MaRDI QIDQ5019209

Mourad Boulsane

Publication date: 3 January 2022

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.00170

zbMATH Keywords

eigenvalueseigenfunctionscircular prolate spheroidal wave functionsfinite Hankel transform operator

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10)

Uses Software

• DLMF

Cites Work

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• The polyanalytic Ginibre ensembles
• Landau's necessary density conditions for the Hankel transform
• Bilinear biorthogonal expansions and the Dunkl kernel on the real line
• Inequalities for the gamma function
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• The finite Hankel transform operator: some explicit and local estimates of the eigenfunctions and eigenvalues decay rates
• High-frequency asymptotic expansions for certain prolate spheroidal wave functions
• Random discretization of the finite Fourier transform and related kernel random matrices
• Approximations for the Bessel and Airy functions with an explicit error term
• Upper bound on √x J_ν(x) and its applications
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - IV: Extensions to Many Dimensions; Generalized Prolate Spheroidal Functions
• Theory of Reproducing Kernels
• Non-asymptotic behavior of the spectrum of the sinc-kernel operator and related applications
• A new bound for the Laguerre polynomials

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