# Continuous abstract wavelet transform on homogeneous space

## TL;DR

This paper investigates the properties of the continuous wavelet transform on homogeneous spaces, revealing its infinite measure support, approximation capabilities, and an analogue of the Heisenberg inequality.

## Contribution

It introduces new theoretical results on wavelet transforms on homogeneous spaces, including measure properties, approximation, and inequalities, expanding understanding of wavelet analysis in this context.

## Key findings

- Wavelet transform support has infinite measure.
- Pointwise homogeneous approximation property established.
- An analogue of Heisenberg inequality derived for wavelet transform.

## Abstract

The support of wavelet transform associated with square integrable irreducible representation of a homogeneous space is shown to have infinite measure. Pointwise homogeneous approximation property for wavelet transform has been investigated. An analogue of Heisenberg type inequality has been also obtained for wavelet transform