Orthonormal spline systems on \(\mathbb R\) with zero means as bases in \(H^1(\mathbb R)\)

DOI10.1007/s10476-017-0504-yzbMath1399.42077OpenAlexW2774829967MaRDI QIDQ682158

K. A. Keryan

Publication date: 13 February 2018

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

Full work available at URL: https://doi.org/10.1007/s10476-017-0504-y

zbMATH Keywords

\(H^1(\mathbb R)\)orthonormal spline system

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10)

Cites Work

• On unconditional basis property in the space \(H^1(\mathbb R)\) of a system of Franklin functions with vanishing means
• The Franklin system is an unconditional basis in \(H_ 1\)
• On the \(L_\infty\)-norm of the orthogonal projector onto splines. A short proof of A. Shadrin's theorem
• On the convergence of odd-degree spline interpolation
• \(H^p\) spaces of several variables
• On a system of piecewise linear functions with vanishing integrals on \(R\)
• On almost everywhere convergence of orthogonal spline projections with arbitrary knots
• General Franklin systems as bases in H¹[0,1]
• A real variable characterization of $H^{p}$
• Unconditionality of general Franklin systems in L^p[0,1, 1<p<∞]
• Unconditionality of orthogonal spline systems in H¹
• Unconditionality of orthogonal spline systems in L^p
• Properties of the orthonormal Franklin system, II
• Properties of the orthonormal Franklin system
• The \(L_\infty\)-norm of the \(L_2\)-spline projector is bounded independently of the knot sequence: A proof of de Boor's conjecture
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