Martingale convergence theorems for tensor splines

DOI10.4064/sm220925-10-11arXiv2101.08971OpenAlexW4390877738WikidataQ130082939 ScholiaQ130082939MaRDI QIDQ6203435

Markus Passenbrunner

Publication date: 28 February 2024

Published in: Studia Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.08971

zbMATH Keywords

Radon-Nikodým propertymaximal functionsalmost everywhere convergencemartingale techniquestensor product spline orthoprojectors

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Generalizations of martingales (60G48) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Spline approximation (41A15) Radon-Nikodým, Kre?n-Milman and related properties (46B22)

Cites Work

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• Uniqueness of Franklin series
• Projections onto piecewise linear functions
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• On almost everywhere convergence of tensor product spline projections
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• On almost everywhere convergence of orthogonal spline projections with arbitrary knots
• An inequality for the Hardy-Littlewood maximal operator with respect to a product of differentiation bases
• Constructive function theory and spline systems
• Spline characterizations of the Radon-Nikodým property
• On the strong derivatives of functions of intervals
• The \(L_\infty\)-norm of the \(L_2\)-spline projector is bounded independently of the knot sequence: A proof of de Boor's conjecture
• Uniqueness of series by generalized Franklin systems

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