Related papers: Extending wavelet regularity beyond Gevrey classes

The establishment of the Wilson-Fisher fixed point (WFP) for $O(n)$ spin models in $d=4-\epsilon$ dimensions stands as a cornerstone of the renormalization group (RG) theory for critical phenomena. However, when long-range (LR)…

Starting from de la Vall\'ee Poussin type (VP) interpolation, the authors have recently introduced a family of interpolating polynomial scaling and wavelet bases generating the approximation and detail spaces of a non-standard…

We show how to extend the Covering Spectrum (CS) of Sormani-Wei to two spectra, called the Extended Covering Spectrum (ECS) and Entourage Spectrum (ES) that are new for Riemannian manifolds but defined with useful properties on any metric…

We study singularly perturbed linear systems of rank two of ordinary differential equations of the form $\hbar x\partial_x \psi (x, \hbar) + A (x, \hbar) \psi (x, \hbar) = 0$, with a regular singularity at $x = 0$, and with a fixed…

We study the persistence of the Gevrey class regularity of solutions to nonlinear wave equations with real analytic nonlinearity. Specifically, it is proven that the solution remains in a Gevrey class, with respect to some of its spatial…

In this paper we use a unified way studying the decay estimate for a class of dispersive semigroup given by $e^{it\phi(\sqrt{-\Delta})}$, where $\phi: \mathbb{R}^+\to \mathbb{R}$ is smooth away from the origin. Especially, the decay…

We study image compression by a separable wavelet basis $\big\{\psi(2^{k_1}x-i)\psi(2^{k_2}y-j),$ $\phi(x-i)\psi(2^{k_2}y-j),$ $\psi(2^{k_1}(x-i)\phi(y-j),$ $\phi(x-i)\phi(y-i)\big\},$ where $k_1, k_2 \in \mathbb{Z}_+$; $i,j\in\mathbb{Z}$;…

This paper addresses the problem of regularity properties of functions represented as an expansion in a wavelet basis with random coefficients in terms of finiteness of their Besov norm with probability 1. Such representations are used to…

We present an extension of the classical De Giorgi class, and then we show that functions in this new class are locally bounded and locally H\"older continuous. Some applications are given. As a first application, we give a regularity…

R measurement results in 2--5 GeV region by BESII is reported in this talk. The study on $\sigma$ particle in $J/\psi \to \omega \pi^+ \pi^-$, based on $7.8 \times 10^6$ BESI $J/\psi$ data, is also reported.

We construct an explicit orthonormal basis of piecewise ${}_{i+1}F_{i}$ hypergeometric polynomials for the Alpert multiresolution analysis. The Fourier transform of each basis function is written in terms of ${}_2F_3$ hypergeometric…

Shape-invariant signals under Fourier transform are investigated leading to a class of eigenfunctions for the Fourier operator. The classical uncertainty Gabor-Heisenberg principle is revisited and the concept of isoresolution in joint…

The $\psi'\to J/\psi\pi^+\pi^-$ decay process provides a new way to extract the $\pi\pi$ $S$ wave phase shifts up to $0.59GeV$. In this paper we derive the formulae for extracting the $\pi\pi$ $S$ wave phase shifts from the invariant mass…

We introduce a method to construct large classes of MSF wavelets of the Hardy space H^2(\R) and symmetric MSF wavelets of L^2(\R), and discuss the classification of such sets. As application, we show that there are uncountably many wavelet…

It is rather unexpected, but true, that it is possible to construct reproducing formulae and orthonormal bases of $L^2 (\mathbb{R}^2)$ just by applying the standard one dimensional wavelet action of translations and dilations to the first…

Given a sampling measure for the wavelet transform (resp. the short-time Fourier transform) with the wavelet (resp. window) being chosen from the family of Laguerre (resp. Hermite) functions, we provide quantitative upper bounds on the…

We study the regularity of Gevrey vectors for H\"ormander operators $$ P = \sum_{j=1}^m X_j^2 + X_0 + c$$ where the $X_j$ are real vector fields and $c(x)$ is a smooth function, all in Gevrey class $G^{s}.$ The principal hypothesis is that…

Many real-world networks are characterized by directionality; however, the absence of an appropriate Fourier basis hinders the effective implementation of graph signal processing techniques. Inspired by discrete signal processing, where…

We analyze representations of solvable Baumslag Solitar group that admit wavelets and show how such representations can be constructed from a given low-pass filter. We describe the direct integral decomposition for some examples and derive…

We prove a smooth and Gevrey-$s$ microlocal hypoellipticity result for a system of complex vector fields associated with a real-analytic locally integrable structure of tube type, that is also microlocal hypocomplex. In order to so, we…