Convolution and Fractional Integration with Measures on Homogeneous Curves in ${\mathbb R}^n$

Convolution and Homogeneous Spaces

convolution and homogeneous spaces

‎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...

Uniform measures and convolution on topological groups

Uniform measures are the functionals on the space of bounded uniformly continuous functions that are continuous on every bounded uniformly equicontinuous set. This paper describes the role of uniform measures in the study of convolution on an arbitrary topological group.

Preferred Parameterisations on Homogeneous Curves

This article is motivated by the theory of distinguished curves in parabolic geometries, as developed in [2]. A parabolic geometry is, by definition, modelled on a homogeneous space of the form G/P where G is a real semisimple Lie group and P is a parabolic subgroup. (There is also a complex theory which corresponds to the choices of complex G’s and P ’s with specific curvature restrictions for...