Frames and Homogeneous Spaces

Abstract

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 the linear operator .

Keywords

• homogeneous spaces
• voice (wavelet) transform
• g?invariant measure
• bessel sequence
• frame