Stationary Measures and Invariant Subsets of Homogeneous Spaces (ii)

‎On the two-wavelet localization operators on homogeneous spaces with relatively invariant measures

In ‎the present ‎paper, ‎we ‎introduce the ‎two-wavelet ‎localization ‎operator ‎for ‎the square ‎integrable ‎representation ‎of a‎ ‎homogeneous space‎ with respect to a relatively invariant measure. ‎We show that it is a bounded linear operator. We investigate ‎some ‎properties ‎of the ‎two-wavelet ‎localization ‎operator ‎and ‎show ‎that ‎it ‎is a‎ ‎compact ‎operator ‎and is ‎contained ‎in‎ a...

Convolution and Homogeneous Spaces

Frames and Homogeneous Spaces

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

A Note on Invariant Finitely Additive Measures

We show that under certain general conditions any finitely additive measure which is defined for all subsets of a set X and is invariant under the action of a group G acting on X is concentrated on a G-invariant subset Y on which the G-action factors to that of an amenable group. The result is then applied to prove a conjecture of S. Wagon about finitely additive measures on spheres. It is well...

On the Structure of the Space of Product - Form

This paper deals with Markovian models which are deened on a nite-dimensional discrete state space, and possess a stationary state distribution of a product-form. We view the space of such models as a mathematical object, and explore its structure. We focus on models on an orthant Z n + , which are homogeneous within subsets of Z n + called walls, and permit only state transitions whose k k 1-l...