On a Refinement Type Equation
نویسنده
چکیده
Let (Ω,A, P ) be a complete probability space. We show that the trivial function is the unique L-solution of the following refinement type equation f(x) = Z Ω |φx(x, ω)|f(φ(x, ω))dP (ω) for a wide class of the given functions φ. This class contains functions of the form φ(x, ω) = α(ω)x−β(ω) with −∞ < R Ω log |α(ω)|dP (ω) < 0.
منابع مشابه
On recursive refinement of convex polygons
It is known that one can improve the accuracy of the finite element solution of partial differential equation (PDE) by uniformly refining a triangulation. Similarly, one can uniformly refine a quadrangulation. Recently a refinement scheme of pentagonal partition was introduced in [4]. It is demonstrated that the numerical solution of Poisson equation based on the pentagonal refinement scheme ou...
متن کاملOn the Numerical Solution of Fourth-Order Linear Two-Point Boundary Value Problems
This paper introduces a fast and numerically stable algorithm for the solution of fourth-order linear boundary value problems on an interval. This type of equation arises in a variety of settings in physics and signal processing. However, current methods of solution involve discretizing the differential equation directly by finite elements or finite differences, and consequently suffer from the...
متن کاملRAMSES: an AMR code of general interest for astrophysics
The RAMSES code, developed under the responsibility of R. Teyssier, is a development platform for solving mainly hyperbolic equation systems in an adaptive mesh refinement structure (AMR). For the time being, the basic mesh is Cartesian. We have planned to extend it to cylindrical and spherical meshing in 2004. The modules that have been developed so far are being massively used in cosmology (p...
متن کاملDevelopment of a parallel Poisson's equation solver with adaptive mesh refinement and its application in field emission prediction
A parallel electrostatic Poisson’s equation solver coupled with parallel adaptive mesh refinement (PAMR) is developed in this paper. The three-dimensional Poisson’s equation is discretized using the Galerkin finite element method using a tetrahedral mesh. The resulting matrix equation is then solved through the parallel conjugate gradient method using the non-overlapping subdomain-by-subdomain ...
متن کاملOn the solving of matrix equation of Sylvester type
A solution of two problems related to the matrix equation of Sylvester type is given. In the first problem, the procedures for linear matrix inequalities are used to construct the solution of this equation. In the second problem, when a matrix is given which is not a solution of this equation, it is required to find such solution of the original equation, which most accurately approximates the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009