Estimates for the SVD of the truncated Fourier transform on \(L^2(\cosh (B|\cdot |))\) and stable analytic continuation
DOI10.1007/s00041-021-09875-6zbMath1471.42011arXiv1905.11338OpenAlexW2946241504MaRDI QIDQ2048694
Eric Gautier, Christophe Gaillac
Publication date: 23 August 2021
Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1905.11338
extrapolationuniform estimatesanalytic continuationsuper-resolutiontruncated Fourier transformnonbandlimited functions
Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Eigenvalue problems for integral equations (45C05) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15) Inverse problems for integral equations (45Q05)
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- Prolate spheroidal wave functions of order zero. Mathematical tools for bandlimited approximation
- Compressed sensing with preconditioning for sparse recovery with subsampled matrices of Slepian prolate functions
- Effective band-limited extrapolation relying on Slepian series and \(\ell^1\) regularization
- Approximate inverse method for stable analytic continuation in a strip domain
- Approximate formulae for certain prolate spheroidal wave functions valid for large values of both order and band-limit
- Analysis and short-time extrapolation of stock market indexes through projection onto discrete wavelet subspaces
- Reconstructing a function from its values on a subset of its domain - a Hilbert space approach
- Efficient estimation of analytic density under random censorship
- Linear integral equations.
- Risk bounds for model selection via penalization
- Sharp inequalities for trigonometric functions
- Quantifying the ill-conditioning of analytic continuation
- Certain inequalities involving prolate spheroidal wave functions and associated quantities
- Uniform bounds of prolate spheroidal wave functions and eigenvalues decay
- Geometric harmonics: a novel tool for multiscale out-of-sample extension of empirical functions
- Asymptotic behavior of the eigenvalues of certain integral equations. II
- Regularization of the ill-posed problem of extrapolation with the Malvar-Wilson wavelets
- Some Extensions of W. Gautschi's Inequalities for the Gamma Function
- A simple regularization method for stable analytic continuation
- A variational approach to the inversion of truncated Fourier operators
- Some comments on Fourier analysis, uncertainty and modeling
- Extrapolating a band-limited function from its samples taken in a finite interval
- Singular Sturm-Liouville Problems: The Friedrichs Extension and Comparison of Eigenvalues
- Functional Inequalities for Hypergeometric Functions and Complete Elliptic Integrals
- On the density of phase-space expansions
- On the best rate of adaptive estimation in some inverse problems
- Some Aspects of Band-Limited Extrapolations
- Stable soft extrapolation of entire functions
- Block Thresholding and Sharp Adaptive Estimation in Severely Ill-Posed Inverse Problems
- Explicit power laws in analytic continuation problems via reproducing kernel Hilbert spaces
- Adaptive Warped Kernel Estimators
- Legendre polynomial kernel estimation of a density function with censored observations and an application to clinical trials
- Some Asymptotic Expansions for Prolate Spheroidal Wave Functions
- Least Squares Methods for Ill-Posed Problems with a Prescribed Bound
- Non-asymptotic behavior of the spectrum of the sinc-kernel operator and related applications
- Ordinary Differential Equations
- Uniform approximation and explicit estimates for the prolate spheroidal wave functions
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