In a previous paper [1] an Euler angle parameterization for SU(4) was given. Here we present the derivation of a generalized Euler angle parameterization for SU(N). The formula for the calculation of the Haar measure for SU(N) as well as its relation to Marinov’s volume formula for SU(N) [2,3] will also be derived. As an example of this parameterization’s usefulness, the density matrix paramete...

in recent years, there has been greater attempt to find numerical solutions of differential equations using wavelet's methods. the following method is based on vector forms of haar-wavelet functions. in this paper, we will introduce one dimensional haar-wavelet functions and the haar-wavelet operational matrices of the fractional order integration. also the haar-wavelet operational matrice...

By superimposing a group structure on a sequence of projective probability spaces of Lebesgue measure preserving (l.m.p.) automorphisms of unit interval, the paper extends the Daniel-Kolmogorov consistency theorem that enables the construction of a measurable group structure with invariant Haar probability measure on an uncountably large projective limit space. The projective limit group is the...

Week 1 (9/7/2010) . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Basic Results and Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Existence of Haar Measure . . . . . . . . . . . . . . . . . . . . . . . . . ...

Let $K$ be a locally compact hypergroup with left Haar measure and let $L^1(K)$ be the complex Lebesgue space associated with it. Let $L^infty(K)$ be the dual of $L^1(K)$. The purpose of this paper is to present some necessary and sufficient conditions for $L^infty(K)^*$ to have a topologically left invariant mean. Some characterizations of amenable hypergroups are given.

We introduce discrete-time linear control systems on connected Lie groups and present an upper bound for the outer invariance entropy of admissible pairs ( K , Q ). If stable subgroup uncontrolled system is closed has positive measure a left invariant Haar measure, coincides with entropy.

In this paper, some known typical properties of function spaces are shown to be prevalent in the sense of the measure-theoretic notion of Haar null.