相关论文: A Class of non-MRA Band-limited Wavelets

In this paper, Meyer wavelets with an arbitrary integer scaling factor $N>2$ are defined using wavelets with multiple scaling factors $MN>2$. Expressions for frequency functions of wavelets and corresponding filters are obtained.

The interplay between symmetry and topology in electronic band structures has been one of the central subjects in condensed-matter physics. Recently, it has been getting clear that a wide variety of useful information about the band…

The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to…

For a given symmetric refinable mask obeying the sum rule of order $n$, an explicit method is suggested for the construction of mutually symmetric almost frame-like wavelet system providing approximation order $n$. A transformation based on…

We establish system of equations for single function normalized tight frame wavelets with compact supports associated with $2\times 2$ expansive integral matrices in $L^2(\R^2)$.

We study the geometric structure of the reproducing kernel Hilbert space associated to the continuous wavelet transform generated by the irreducible representations of the Euclidean Motion $SE(2)$. A natural Hilbert norm for functions on…

In this paper, we introduce a notion of weak pointwise Holder regularity, starting from the de nition of the pointwise anti-Holder irregularity. Using this concept, a weak spectrum of singularities can be de ned as for the usual pointwise…

In this article, the author establishes a wavelet characterization of inhomogeneous Lipschitz space $\mathrm{lip}_{\theta}(\mathcal{X})$ via Carlson sequence, where $\mathcal{X}$ is a space of homogeneous type introduced by R. R. Coifman…

For the wavelet type orthonormal systems $\phi_n$, we establish a new bound \begin{equation} \left\|\max_{1\le m\le n}\left|\sum_{j\in G_m}\langle f,\phi_j\rangle \phi_j\right|\right\|_p\lesssim \sqrt{\log (n+1)}\cdot \|f\|_p,\quad…

In this paper, we classify the spherically symmetric Berwald metrics in $\mathbb{R}^n$. For the spherically symmetric Landsberg metrics, we prove that there do not exist any non-Berwald metrics among the regular case. The partial…

We define a set of operators that localise a radial image in radial space and radial frequency simultaneously. We find the eigenfunctions of this operator and thus define a non-separable orthogonal set of radial wavelet functions that may…

We characterize the scaling function of a crystal Multiresolution Analysis in terms of the vector-scaling function for a Multiresolution Analysis associated to a lattice. We give necessary and sufficient conditions in terms of the symbol…

In this short paper we discuss how the position - scale half-space of wavelet analysis may be cut into different regions. We discuss conditions under which they are independent in the sense that the T\"oplitz operators associated with their…

In this note we announce that under general hypotheses, wavelet-type expansions (of functions in $L^p,\ 1\leq p \leq \infty$, in one or more dimensions) converge pointwise almost everywhere, and identify the Lebesgue set of a function as a…

We study a class of localized solutions of the wave equation, called eigenwavelets, obtained by extending its fundamental solutions to complex spacetime in the sense of hyperfunctions. The imaginary spacetime variables y, which form a…

We here use notions from the theory linear shift-invariant dynamical systems to provide an easy-to-compute characterization of all rational wavelet filters. For a given N bigger or equql to 2, the number of inputs, the construction is based…

Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two…

We initiate the construction of integrable $\lambda$-deformed WZW models based on non-semisimple groups. We focus on the four-dimensional case whose underlying symmetries are based on the non-semisimple group $E_2^c$. The corresponding…

A basis of $N^2$ projectors, each an ${N^2}\times{N^2}$ matrix with constant elements, is implemented to construct a class of braid matrices $\hat{R}(\theta)$, $\theta$ being the spectral parameter. Only odd values of $N$ are considered…

In this paper, we introduce a wavelet-based method for estimating the EDR space in Li's semiparametric regression model for achieving dimension reduction. This method is obtained by using linear wavelet estimators of the density and…