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Non-parametric function estimation aims to estimate or recover or denoise a function of interest, perhaps a signal, spectrum or image, that is observed in noise and possibly indirectly after some tr...
Using the Walsh-Fourier transform, we give a construction of compactly supported nonstationary dyadic wavelets on the positive half-line. The masks of these wavelets are the Walsh polynomials defined ...
Abstract: A wavelet is a localized function having a prescribed number of vanishing moments. In this correspondence, we provide precise arguments as to why the Hilbert transform of a wavelet is again ...
Given a real, expansive dilation matrix we prove that any bandlimited function ∈ L2(Rn), for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame for cer...
Dual pseudo splines constitute a new class of refinable functions with B-splines as special examples, which was introduced in [8]. In this paper, we shall construct Riesz wavelet associated with dual ...
We use the continuous Legendre multi-wavelets on the interval [0, 1) to solve the linear integro-differential equation. To do so, we reduced the problem into a system of algebraic equations. Illustrat...
In this paper we present general constructions of orthogonal and biorthogonal multiresolution analysis on the interval. In the first one, we describe a direct method to define an orthonormal multire...
In 2000, Papadakis announced that any orthonormal wavelet must be derived by a generalized frame MRA (GFMRA). In this paper, we give a characterization of GFMRAs which can derive orthonormal wavelets,...
The construction of frame wavelets with compact supports is a meaningful problem in wavelet analysis. In particular, it is a hard work to construct the frame wavelets with explicit analytic forms. For...
Given a multiresolution analysis of multidimension, we construct pre-wavelets and a Rieszwavelet basis under some assumptions on the scale function. Example are provided.

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