Localized bases in \(L^2(0,1)\) and their use in the analysis of Brownian motion

DOI10.1016/j.jat.2007.08.002zbMath1142.42016arXivmath/0512659OpenAlexW2021269234MaRDI QIDQ2481509

Anilesh Mohari, Palle E. T. Jorgensen

Publication date: 10 April 2008

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

Full work available at URL: https://arxiv.org/abs/math/0512659

zbMATH Keywords

waveletsHilbert spaceCantor setorthonormal basisiterated function systemCuntz relationsWalshHaarirreductible representation

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Abstract operator algebras on Hilbert spaces (47L30) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Geometric limits in holomorphic dynamics (37F40)

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Cites Work

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• Wavelets on fractals
• Simple \(C^*\)-algebras generated by isometries
• Unitary representations of Lie groups with reflection symmetry
• Dense analytic subspaces in fractal \(L^2\)-spaces
• Harmonic analysis and fractal limit-measures induced by representations of a certain \(C^*\)-algebra
• A quantum computing primer for operator theorists
• Wavelets, generalized white noise and fractional integration: The synthesis of fractional Brownian motion
• Heisenberg groups -- a unifying structure of signal theory, holography and quantum information theory
• Harmonic analysis of fractal measures
• Frames, graphs and erasures
• Some equations relating multiwavelets and multiscaling functions
• Measures in wavelet decompositions
• A class of generalized Walsh functions
• Universal collective rotation channels and quantum error correction
• On a Certain Class of Operator Algebras
• Iterated function systems, Ruelle operators, and invariant projective measures
• Construction of Parseval wavelets from redundant filter systems
• Ten Lectures on Wavelets
• Hilbert spaces of martingales supporting certain substitution-dynamical systems
• Geometric aspects of frame representations of abelian groups
• Endomorphisms of B(H)
• Entropy-based algorithms for best basis selection
• Wavelets