The octonionic Fourier transform: Uncertainty relations and convolution

The uncertainty principle is a fundamental principle in mathematics and physics, and also plays an important role in signal processing. On the other side, the octonion Fourier transform has got a lot of attentions in recent years. It is the aim of this paper to establish various uncertainty relations for this new hyper-complex Fourier transform. Based on the relations between the octonion Fourier transform and the quaternion Fourier transform, several uncertainty inequalities are derived neatly, including the logarithmic uncertainty inequality, local uncertainty inequalities, generalized global uncertainty inequality and the Benedicks-Amrein-Berthier inequality. In addition, the Mustard convolution associated to the octonion Fourier transform is discussed as well. (C) 2019 Elsevier B.V. All rights reserved.