Distributional Solutions of Nonhomogeneous
نویسنده
چکیده
Discrete and continuous refinement equations have been widely studied in the literature for the last few years, due to their applications to the areas of wavelet analysis and geometric modeling. However, there is no “universal” theorem that deals with the problem about the existence of compactly supported distributional solutions for both discrete and continuous refinement equations simultaneously. In this paper, we provide a uniform treatment for both equations. In particular, a complete characterization of the existence of distributional solutions of nonhomogeneous discrete and continuous refinement equations is given, which covers all cases of interest.
منابع مشابه
Distributional Solutions of Nonhomogeneous Discrete and Continuous Refinement Equations
Discrete and continuous reenement equations have been widely studied in the literature for the last few years, due to their applications to the areas of wavelet analysis and geometric modeling. However, there is nòuniversal' theorem that deals with the problem about the existence of compactly supported distributional solutions for both discrete and continuous reenement equations simultaneously....
متن کاملCompactly Supported Distributional Solutions of Nonstationary Nonhomogeneous Reenement Equation
Let A be a matrix with the absolute values of all eigenvalues strictly larger than one, and let Z 0 be a subset of Z such that n 2 Z 0 implies n + 1 2 Z 0. Denote the space of all compactly supported distributions by D 0 , and the usual convolution between two compactly supported distributions f and g by f g.
متن کاملThe distributional Henstock-Kurzweil integral and measure differential equations
In the present paper, measure differential equations involving the distributional Henstock-Kurzweil integral are investigated. Theorems on the existence and structure of the set of solutions are established by using Schauder$^prime s$ fixed point theorem and Vidossich theorem. Two examples of the main results paper are presented. The new results are generalizations of some previous results in t...
متن کاملMathematical Modeling of Thermoelastic State of a Thick Hollow Cylinder with Nonhomogeneous Material Properties
The object of the present paper is to study heat conduction and thermal stresses in a hollow cylinder with nonhomogeneous material properties. The cylinder is subjected to sectional heating at the curved surface. All the material properties except for Poisson’s ratio and density are assumed to be given by a simple power law in the axial direction. A solution of the two-dimensional heat conducti...
متن کاملThe existence of solutions to the nonhomogeneous A - harmonic equation
* Correspondence: mathwy@hit. edu.cn Department of Mathematics, Harbin Institute of Technology, Harbin 150001, People’s Republic of China Abstract In this paper, we introduce the obstacle problem about the nonhomogeneous A-harmonic equation. Then, we prove the existence and uniqueness of solutions to the nonhomogeneous A-harmonic equation and the obstacle problem.
متن کامل