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Characterization of scaling functions in a multiresolution analysis
We characterize the scaling functions of a multiresolution analysis in a general context, where instead of the dyadic dilation one considers the dilation given by a fixed linear map A: R n → R n suchExpand
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Characterization of scaling functions
We give a complete characterization of functions � 2 L 2 (R n ), which generate frame multiresolution analyses. The char- acterization of scaling functions of a multiresolution analysis is de- ducedExpand
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Spline Wavelet Bases of Weighted L p Spaces, 1 ≤p < ∞
We study necessary conditions on the weight w for the spline wavelet systems to be bases in the weighted space LP (w) . In this article we study some questions arising in the investigation of theExpand
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Stopping Times and Local Convergence for Spline Wavelet Expansions
TLDR
A local convergence theorem for spline wavelet expansions is proved. Expand
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Vector-valued Hausdorff-Young inequality and applications
Contents §1. Introduction §2. General definitions and auxiliary results §3. Interpolation spaces §4. Interpolation and the Fourier type of Banach spaces §5. The Rademacher type and cotype §6. TheExpand
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Wavelets in weighted norm spaces
We give a complete characterization of the classes of weight functions for which the Haar wavelet system for $m$-dilations, $m= 2,3,\ldots$ is an unconditional basis in $L^p(\mathbb{R},w)$.Expand
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