Continuous wavelet transforms on the space L2(R, H;dx)

Abstract Let P be the affine group of the real line R, and let H be the set of all quaternions. Thus, L2 (R, H ; dx) denotes the space of all square integrable H -valued functions. From the viewpoint of square integrable group representations, we study the theory of continuous wavelet transforms on L2(R, H ; dx) associated with the group P, and give the Calderon reproducing formula.