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 such… Expand

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- duced… Expand

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 the… Expand

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. The… Expand

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