Geometric algebra integral transforms and their applications
Abstract
In geometric algebra (GA), real and complex integral transforms (Fourier transforms, linear canonical transforms (LCTs), wavelets, fractional Fourier transforms, special affine Fourier transforms, etc.) can be generalized to holistic higher-dimensional quaternionic, octonionic and Clifford GA versions. This review introduces the foundations of these generalizations, provides representative examples of these new types of transforms and refers to some of their applications in mathematics, physics and engineering. This article is part of the theme issue 'Modern applications of geometric algebra'.
Fields of Study & Subjects
Algebraic and Geometric Analysis
Mathematical Analysis and Transform Methods
Advanced Algebra and Geometry
Publication details
- Journal / source
- Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences
- Publisher
- The Royal Society
- Volume
- 384
- Issue
- 2326
- Publication date
- 13 August 2026
- Language
- EN