The limiting behavior of certain sampling series and cardinal splines

DOI10.1016/j.jat.2019.105298zbMath1434.94044OpenAlexW2978810356WikidataQ127215863 ScholiaQ127215863MaRDI QIDQ2007607

W. R. Madych

Publication date: 22 November 2019

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

Full work available at URL: https://doi.org/10.1016/j.jat.2019.105298

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Interpolation in approximation theory (41A05) Spline approximation (41A15) Sampling theory in information and communication theory (94A20)

Related Items (2)

Sampling Series, Refinable Sampling Kernels, and Frequency Band Limited Functions ⋮ Local and global phaseless sampling in real spline spaces

Cites Work

• Convergence of classical cardinal series and band limited special functions
• Cardinal interpolation with general multiquadrics
• Polyharmonic cardinal splines
• A modification of the Whittaker-Kotelnikov-Shannon sampling series
• Symmetric iterative interpolation processes
• Miscellaneous error bounds for multiquadric and related interpolators
• Cardinal interpolation and spline functions. VII: The behavior of cardinal spline interpolants as their degree tends to infinity
• Convergence of interpolating cardinal splines: power growth
• The behavior of polyharmonic cardinal splines as their degree tends to infinity
• Notes on spline functions. IV: A cardinal spline analogue of the theorem of the brothers Markov
• On the convergence of regular families of cardinal interpolators
• Five short stories about the cardinal series
• Convergence of Cardinal Series
• The Shannon sampling theorem—Its various extensions and applications: A tutorial review
• A Remainder Formula and Limits of Cardinal Spline Interpolants
• Sampling procedures in function spaces and asymptotic equivalence with shannon's sampling theory
• On the regularized Whittaker-Kotel’nikov-Shannon sampling formula
• Summability of cardinal series and of localized fourier series
• Convergence of Classical Cardinal Series
• On cardinal interpolation by Gaussian radial-basis functions: Properties of fundamental functions and estimates for Lebesgue constants
• Summability of Lagrange type interpolation series
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