Extrapolation methods and Rubio de Francia's extrapolation theorem

Weighted Weak-type (1, 1) Estimates via Rubio De Francia Extrapolation

The classical Rubio de Francia extrapolation result asserts that if an operator T : L0(u) → Lp0,∞(u) is bounded for some p0 > 1 and every u ∈ Ap0 , then, for every 1 < p < ∞ and every u ∈ Ap, T : L(u) → Lp,∞(u) is bounded. However, there are examples showing that it is not possible to extrapolate to the end-point p = 1. In this paper we shall prove that there exists a class of weights, slightly...

Extensions: Extrapolation Methods for CAD

Many operations within a solid modeling application, notably applying thickness (shelling) or blending edges ( lleting), encounter di culties during topology resolution. In order to create a solid object, certain faces have to be intersected but the geometry is such that no intersection curve can be computed. The solution is to "extend" one or both faces. This means that one has to extrapolate ...

Extrapolation Methods in Mathematica 1

This article outlines design and implementation details of the framework for one step methods for solving ordinary differential equations in Mathematica. The solver breaks up the solution into three main phases for equation processing and classification, numerical solution and processing of results. One of the distinguishing features of the framework is the hierarchical nature of the method inv...

On a Boundary Extrapolation Theorem by Kreiss

A hardly known and very important result of Kreiss is proven explicitly: Outflow boundary extrapolation, which complements stable dissipative schemes for linear hyperbolic initial value problems, maintains stability. In view of this result, the Lax-Wendroff and the Gottlieb-Turkel schemes are applied to a test problem. As expected from the rate-of-convergence theory by Gustafsson, global order ...

On the Range Space of Yano’s Extrapolation Theorem and New Extrapolation Estimates at Infinity