From Haar to Lebesgue via Domain Theory, Revised version

From Haar to Lebesgue via Domain Theory

Solving infinite horizon optimal control problems of nonlinear interconnected large-scale dynamic systems via a Haar wavelet collocation scheme

We consider an approximation scheme using Haar wavelets for solving a class of infinite horizon optimal control problems (OCP's) of nonlinear interconnected large-scale dynamic systems. A computational method based on Haar wavelets in the time-domain is proposed for solving the optimal control problem. Haar wavelets integral operational matrix and direct collocation method are utilized to find ...

A Property of the Haar Measure of Some Special LCA Groups

The Euclidean group (Rn,+) where (n?N, plays a key role in harmonic analysis. If we consider the Lebesgue measure ()nd?xR as the Haar measure of this group then 12(2)()nd?x=d?RR. In this article we look for LCA groups K, whose Haar measures have a similar property. In fact we will show that for some LCA groups K with the Haar measure K?, there exists a constant such that 0KC>()(2)KKK?A=C?A for ...

Measure Theory

These are some brief notes on measure theory, concentrating on Lebesgue measure on Rn. Some missing topics I would have liked to have included had time permitted are: the change of variable formula for the Lebesgue integral on Rn; absolutely continuous functions and functions of bounded variation of a single variable and their connection with Lebesgue-Stieltjes measures on R; Radon measures on ...

Haar-like wavelets defined over tetrahedrical grids - Computer Science Society, 2000. Proceedings. XX International Conference of the Chilean

In this paper we systematically define Haar-like wavelets over a tetrahedrical grid which is generated b y a regular subdivision method. These wavelets form an inconditional basis for LJ'(T,C,p), 1 < p < 00 , being p the Lebesgue measure and C the U-algebra of all tetrahedra generated from a tetrahedron T by the chosen subdivision method.