On the sampling and recovery of bandlimited functions via scattered translates of the Gaussian

DOI10.1016/j.jat.2009.02.007zbMath1166.42017arXiv0803.4344OpenAlexW1982022302MaRDI QIDQ2389531

N. Sivakumar, Thomas Schlumprecht

Publication date: 17 July 2009

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0803.4344

zbMATH Keywords

scattered dataGaussian interpolationbandlimited function

Mathematics Subject Classification ID

General harmonic expansions, frames (42C15) Approximations and expansions (41A99)

Related Items (15)

Convergence and Regularization of Sampling Series ⋮ Cardinal interpolation with general multiquadrics: convergence rates ⋮ Nonuniform sampling and recovery of bandlimited functions in higher dimensions ⋮ Recovery of Paley-Wiener functions using scattered translates of regular interpolators ⋮ Error estimates of quasi-interpolation and its derivatives ⋮ Sampling and Average Sampling in Quasi Shift-Invariant Spaces ⋮ Approximation rates for interpolation of Sobolev functions via Gaussians and allied functions ⋮ Recovery of bivariate band-limited functions using scattered translates of the Poisson kernel ⋮ Convergence of classical cardinal series and band limited special functions ⋮ On the structure and interpolation properties of quasi shift-invariant spaces ⋮ Nonuniform sampling and recovery of multidimensional bandlimited functions by Gaussian radial-basis functions ⋮ Limit properties of systems of integer translates and functions generating tight Gabor frames ⋮ Stability and Robustness of RBF Interpolation ⋮ Average sampling and reconstruction in shift-invariant spaces and variable bandwidth spaces ⋮ On the Riesz constants for systems of integer translates

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Propriétés des matrices ``bien localisées près de leur diagonale et quelques applications. (Properties of matrices ``well localized near the diagonal and some applications)
• Norm estimates for the inverses of a general class of scattered-data radial-function interpolation matrices
• Classical Fourier transforms
• The recovery of irregularly sampled band limited functions via tempered splines
• On condition numbers associated with radial-function interpolation
• Gaussian radial-basis functions: cardinal interpolation of \(\ell^p\) and power-growth data
• Restrictions of Fourier transforms and extension of Fourier sequences
• On shifted cardinal interpolation by Gaussians and multiquadrics
• A sampling theorem for irregularly spaced sample points (Corresp.)
• Cardinal interpolation by Gaussian functions: A survey
• On cardinal interpolation by Gaussian radial-basis functions: Properties of fundamental functions and estimates for Lebesgue constants

This page was built for publication: On the sampling and recovery of bandlimited functions via scattered translates of the Gaussian