Convergence of biorthogonal series in the system of contractions and translations of functions in the spaces \(L^p[0, 1]\)

DOI10.1134/S000143460805009XzbMath1159.42018MaRDI QIDQ2518024

Pavel A. Terekhin

Publication date: 12 January 2009

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

Haar functionswavelet theorybiorthogonal series\(L^p[0,1\)]bundle convergence of Fourier-Haar seriesseries of contractions and translations of a function

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) Function spaces arising in harmonic analysis (42B35) Convergence and divergence of series and sequences of functions (40A30) General harmonic expansions, frames (42C15) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58)

Related Items (3)

Riesz basicity for general systems of functions ⋮ Affine System of Walsh Type. Completeness and Minimality ⋮ Affine Bessel sequences and Nikishin’s example

Cites Work

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• A general framework of compactly supported splines and wavelets
• Wavelets on the interval and fast wavelet transforms
• On perturbations of the Haar system
• Representation in \(L_ p\) by series of translates and dilates of one function
• Multishifts in Hilbert spaces
• Ten Lectures on Wavelets
• Periodic wavelets
• Tauberian theorems

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