In this paper we consider the new concept of the quaternionic unitary representation of a locally compact group to the unitary group of a quaternionic Hilbert space, and study its properties. Also, we establish a continuous wavelet transform...

For homogeneous space G/H equipped with strongly quasi invariant measure ν, we introduce the two-wavelet constant for square integrable representations and the orthogonal subspaces of L2(G/H), which are related to continuous wavelet transform (C...