Admissible wavelets on groups and their homogeneous spaces

F Esmaeelzadeh,R A Kamyabi Gol

doi:10.12988/pms.2014.3713

Abstract

In this note, let G be a locally compact group and H be a compact subgroup of G. We investigate the square integrable representations of homogeneous spaces G/H and admissible wavelets for these representations. Also, we consider the relation between the square integrable representations of locally compact groups and their homogeneous spaces. Moreover, the connection between existence of admissible wavelets for locally compact groups and their homogeneous spaces is described.

Highlights

Introduction and PreliminariesFor a locally compact group G with left Haar measure λ it is well known that a continuous unitary representation π of G is called square integrable if there exists a non-zero vector ζ in Hilbert space H such that| < π(x)ζ, ζ > |2dλ(x) < ∞
The square integrable representations on homogeneous spaces that admit G-invariant measure and relatively invariant measure have been studied in [1, 5]. In this manuscript we investigate the relation between square integrable representations of locally compact group G and its homogeneous space G/H, in which H is compact subgroup of G
In this paper we introduce square integrable representations of homogeneous space G/H equiped with a relatively invariant measure μ

Summary

Esmaeelzadeh

Copyright c 2014 F. Esmaeelzadeh and R. A. Kamyabi Gol. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Introduction and Preliminaries

Main Result