Affiliation:
1. School of Computer Science and Engineering, Faculty of Innovation Engineering Macau University of Science and Technology Macau China
2. Department of Engineering Science, Faculty of Innovation Engineering Macau University of Science and Technology Macau China
Abstract
In this paper, we revisit some fundamental properties of linear canonical transform (abbreviated as LCT). In particular, we prove the additive property rigorously for LCT in the higher dimensional case (abbreviated as MLCT). We also consider the
‐theory of MLCT with
. Specifically, the inversion theorem of MLCT by the related Gauss and Abel means is studied, and the pointwise convergence of approximate identities with respect to convolution for MLCT is also obtained. As applications, we study the
‐type Heisenberg‐Pauli‐Weyl uncertainty principles and the
‐type Donoho‐Stark uncertainty principles for MLCT.
Funder
Fundo para o Desenvolvimento das Ciências e da Tecnologia
Macau University of Science and Technology Foundation
National Natural Science Foundation of China
Subject
General Engineering,General Mathematics