Results 11 to 20 of about 363 (235)

Approximation by crystal-refinable functions [PDF]

Geometriae Dedicata, 2019
Let $ $ be a crystal group in $\mathbb R^d$. A function $ :\mathbb R^d\longrightarrow \mathbb C$ is said to be {\em crystal-refinable} (or $ -$refinable) if it is a linear combination of finitely many of the rescaled and translated functions $ ( ^{-1}(ax))$, where the {\em translations} $ $ are taken on a crystal group $ $, and $a$ is an ...
Ursula Molter, María del Carmen Moure, Alejandro Quintero   +2 more
openaire   +4 more sources

Refinable Trapezoidal Method on Riemann–Stieltjes Integral and Caputo Fractional Derivatives for Non-Smooth Functions

Fractal and Fractional, 2023
The Caputo fractional α-derivative ...
Gopalakrishnan Karnan, Chien-Chang Yen
doaj   +1 more source

Analysis and construction of a family of refinable functions based on generalized Bernstein polynomials

Journal of Inequalities and Applications, 2016
In this paper, we construct a new family of refinable functions from generalized Bernstein polynomials, which include pseudo-splines of Type II. A comprehensive analysis of the refinable functions is carried out.
Ting Cheng, Xiaoyuan Yang
doaj   +1 more source

Construction of a family of non-stationary biorthogonal wavelets

Journal of Inequalities and Applications, 2019
The family of exponential pseudo-splines is the non-stationary counterpart of the pseudo-splines and includes the exponential B-spline functions as special members.
Baoxing Zhang, Hongchan Zheng, Jie Zhou, Lulu Pan   +3 more
doaj   +1 more source

A Brief Survey of the Graph Wavelet Frame

Complexity, 2022
In recent years, the research of wavelet frames on the graph has become a hot topic in harmonic analysis. In this paper, we mainly introduce the relevant knowledge of the wavelet frames on the graph, including relevant concepts, construction methods, and
Jie Zhou, Zeze Zhang
doaj   +1 more source

Analysis of Compactly Supported Nonstationary Biorthogonal Wavelet Systems Based on Exponential B-Splines

Abstract and Applied Analysis, 2011
This paper is concerned with analyzing the mathematical properties, such as the regularity and stability of nonstationary biorthogonal wavelet systems based on exponential B-splines.
Yeon Ju Lee, Jungho Yoon
doaj   +1 more source

Orhonormal Wavelet Bases on The 3D Ball Via Volume Preserving Map from the Regular Octahedron

Mathematics, 2020
We construct a new volume preserving map from the unit ball B 3 to the regular 3D octahedron, both centered at the origin, and its inverse. This map will help us to construct refinable grids of the 3D ball, consisting in diameter bounded cells ...
Adrian Holhoş, Daniela Roşca
doaj   +1 more source

Construction of Compactly Supported Refinable Componentwise Polynomial Functions in ℝ2

Abstract and Applied Analysis, 2011
We provide a sufficient condition for constructing a class of compactly supported refinable functions with componentwise polynomial property in ℝ2. An iteration algorithm is developed to compute the polynomial on each component of the functions' support.
Yanmei Xue, Ning Bi
doaj   +1 more source

Quincunx Fundamental Refinable Functions in Arbitrary Dimensions

Axioms, 2017
In this paper, we generalize the family of Deslauriers–Dubuc’s interpolatory masks from dimension one to arbitrary dimensions with respect to the quincunx dilation matrices, thereby providing a family of quincunx fundamental refinable functions in ...
Xiaosheng Zhuang
doaj   +1 more source

The regularity of refinable functions

Applied and Computational Harmonic Analysis, 2013
The regularity of refinable functions has been studied extensively in the past. A classical result by Daubechies and Lagarias states that a compactly supported refinable function in $\R$ of finite mask with integer dilation and translations cannot be in $C^\infty$.
Wang, Yang, Xu, Zhiqiang
openaire   +3 more sources