Atomic functions: generalization to the multivariable case and promising applications

DOI10.1007/s10559-007-0114-yzbMath1151.35301OpenAlexW2005408372MaRDI QIDQ941207

V. A. Rvachov, V. M. Kolodyazhny

Publication date: 4 September 2008

Published in: Cybernetics and Systems Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10559-007-0114-y

zbMATH Keywords

functional-differential equationatomic functionatomic function of many variablescompactly supported function

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Development of contemporary mathematics (01A65) Approximation by other special function classes (41A30) Functional-differential equations (including equations with delayed, advanced or state-dependent argument) (34K99) History of partial differential equations (35-03)

Related Items (5)

Hilbert and Riesz transforms using atomic function for quaternionic phase computation ⋮ Controllability problem for the string equation with external load with the use of atomic functions ⋮ Symmetry feature extraction based on quaternionic local phase ⋮ Maximum entropy algorithm with inexact upper entropy bound based on \(Fup\) basis functions with compact support ⋮ Quaternionic Local Phase for Low-level Image Processing Using Atomic Functions

Cites Work

• Refinement differential equations and wavelets
• Multiresolution analysis by infinitely differentiable compactly supported functions
• Synthesis of weight windows on the basis of atomic functions
• Interpolating scaling functions, Bernstein polynomials and nonstationary wavelets
• Meshless methods: An overview and recent developments
• An algorithm for the construction of wavelet systems for signal processing
• Orthonormal wavelet systems based on atomic functions
• Functional and algorithmic descriptions of geometric distinctive features of shaped castings in modeling casting processes
• On the construction of multivariate (pre)wavelets
• Approximations by atomic functions and numerical methods for Fredholm integral equations of the second kind
• Generalized refinement equations and subdivision processes
• On infinitely smooth compactly supported almost-wavelets
• Solving differential equations with radial basis functions: Multilevel methods and smoothing
• Subdivision schemes in geometric modelling
• Compactly supported solutions of functional-differential equations and their applications
• Ten Lectures on Wavelets
• Method of R-functions in boundary-value problems
• Basic wavelet theory
• Spectral properties of continuous refinement operators
• Radial Basis Functions
• Survey of meshless and generalized finite element methods: A unified approach
• Distributional Solutions of Nonhomogeneous Discrete and Continuous Refinement Equations
• Combinatorics for Wavelets: The Umbral Refinement Equation
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Atomic functions: generalization to the multivariable case and promising applications