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

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