A Note on Moritoh Transforms

Some fundamental properties of the Moritoh wavelet are discussed in this paper. The Moritoh transform is approximated for ultra-distributions in generalised Sobolev space. The adjoint formula of the Fourier transform is extended to the Moritoh transform. The convolution for quaternion-valued functions is defined for a modified representation of quaternions. Furthermore, the quaternionic Moritoh transform is defined with the help of convolution. The inner product relation and the uncertainty principle are also established for the quaternionic Moritoh wavelet transform.