  In the last decade, methods based on various kinds of spherical wavelet bases
have found applications in virtually all areas where analysis of spherical data
is required, including cosmology, weather prediction, and geodesy. In
particular, the so-called needlets (=band-limited Parseval frames) have become
an important tool for the analysis of Cosmic Microwave Background (CMB)
temperature data. The goal of the present paper is to construct band-limited
and highly localized Parseval frames on general compact homogeneous manifolds.
Our construction can be considered as an analogue of the well-known
phi-transform on Euclidean spaces.
