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Tight framelets on a smooth and compact Riemannian manifold $\mathcal{M}$ provide a tool of multiresolution analysis for data from geosciences, astrophysics, medical sciences, etc. This work investigates the construction, characterizations,…
We present a new adaptive circuit simulation algorithm based on spline wavelets. The unknown voltages and currents are expanded into a wavelet representation, which is determined as solution of nonlinear equations derived from the circuit…
In a previous paper we have introduced a new class of radial basis functions that are powerful means to approximate functions by quasi-interpolation. In this article we extend the results to create new ways of approximating functions by…
This paper is devoted to the study of a problem of Cassels in multiplicative Diophantine approximation which involves minimising values of a product of affine linear forms computed at integral points. It was previously known that values of…
Discrete wavelets are applied to parametrization of the intra-chain two-point correlation functions of homopolymers in dilute solutions obtained from Monte Carlo simulation. Several orthogonal and biorthogonal basis sets have been…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
In this work, we propose a class of spline-like wavelet filterbanks for graph signals. These filterbanks possess the properties of critical sampling and perfect reconstruction. Besides, the analysis filters are localized in the graph domain…
The article proposes a novel near-field predictive beamforming framework for high-mobility wireless networks. Specifically, due to the spherical waves and non-uniform Doppler frequencies brought by the near-field region, the new ability of…
A new method is presented for the construction of a natural continuous wavelet transform on the sphere. It incorporates the analysis and synthesis with the same wavelet and the definition of translations and dilations on the sphere through…
In pump-probe spectroscopy, one often needs to analyse the transmission or reflection of electromagnetic waves through optically pumped media. Here, it is common practice to approximate the analysis in order to extract non-equilibrium…
In this paper we present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to variational approach in the general case we have the solution as a…
Factorization of matrices of Laurent polynomials plays an important role in mathematics and engineering such as wavelet frame construction and filter bank design. Wavelet frames (a.k.a. framelets) are useful in applications such as signal…
Inspired by edge detection based on the decay behavior of wavelet coefficients, we introduce a (near) linear-time algorithm for detecting the local regularity in non-uniformly sampled multivariate signals. Our approach quantifies regularity…
We provide a characterization of wavelets on local fields of positive characteristic based on results on affine and quasi affine frames. This result generalizes the characterization of wavelets on Euclidean spaces by means of two basic…
We proved that for any matrix dilation and for any positive integer $n$, there exists a compactly supported tight wavelet frame with approximation order $n$. Explicit methods for construction of dual and tight wavelet frames with a given…
This paper develops the use of wavelets as a basis set for the solution of physical problems exhibiting behavior over wide-ranges in length scale. In a simple diagrammatic language, this article reviews both the mathematical underpinnings…
Starting with a regular symmetric Dirichlet form on a locally compact separable metric space $X$, our paper studies elements of vector analysis, $L_p$-spaces of vector fields and related Sobolev spaces. These tools are then employed to…
This paper reviews two different uses of the continuous wavelet transform for modal identification purposes. The properties of the wavelet transform, mainly energetic, allow to emphasize or filter the main information within measured…
In this paper orthogonal multifilters for astronomical image processing are presented. We obtained new orthogonal multifilters based on the orthogonal wavelet of Haar and Daubechies. Recently, multiwavelets have been introduced as a more…
Dense flow visualization is a popular visualization paradigm. Traditionally, the various models and methods in this area use a continuous formulation, resting upon the solid foundation of functional analysis. In this work, we examine a…