Mawardi Bahri, Nasrullah Bachtiar, Muhammad Nur, Amran Rahim
We introduce a generalized quaternion Fourier transform termed the linear canonical space-time transform (LCST). The uncertainty principles and convolution theorem are the prominent results that play a significant role in the development of the LCST, both theoretically and in its applications. This study explores the convolution theorem and then establish two uncertainty principles associated with the proposed transformation. In addition, we rigorously derive a new point-wise Heisenberg-type uncertainty inequality for the LCST and special cases of this new Heisenberg principle are also presented. © The Author(s) under exclusive license to Università degli Studi di Ferrara 2026.
Department of Mathematics, Hasanuddin University, Makassar, 90245, Indonesia; Department of Actuarial Science, Sumatera Institute of Technology, Lampung, Indonesia