\(\ell^1\)-summability and Fourier series of B-splines with respect to their knots

DOI10.1007/s00209-024-03440-9arXiv2208.02167OpenAlexW4391915107MaRDI QIDQ6123043

Janin Jäger, Martin D. Buhmann, Yuan Xu

Publication date: 4 March 2024

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.02167

zbMATH Keywords

biorthogonalityFourier seriespositive definite functionB-spline function\(\ell^1\)-invariant

Mathematics Subject Classification ID

Spline approximation (41A15) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) (42A32)

Cites Work

• On multivariate de la Vallée Poussin-type projection operators
• \(\ell _{1}\)-summability of higher-dimensional Fourier series
• Strictly positive definite kernels on the torus
• Christoffel functions and Fourier series for multivariate orthogonal polynomials
• Fejér means for multivariate Fourier series
• Lebesgue points of \(\ell_1\)-Cesàro summability of \(d\)-dimensional Fourier series
• On multivariate projection operators
• l-1 summability of multiple Fourier integrals and positivity
• Summability of Multi-Dimensional Trigonometric Fourier Series

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