The continuous quaternion algebra-valued wavelet transform and the associated uncertainty principle (Q2066086)

Let \(\mathbb H\) be the quaternion algebra over \(\mathbb R\). For square-integrable, bivariate functions \(f: {\mathbb R}^2 \to \mathbb H\) the author considers the two-dimensional quaternion Fourier transform. Based on this Fourier transform, he introduces a two-dimensional continuous wavelet transform. For this wavelet transform, he proves some properties such as Parseval's identity, scaling, translation, and rotation properties. Further a generalized uncertainty principle for the two-dimensional continuous quaternion wavelet transform is formulated.