Quaternion and Clifford Fourier Transforms

The book begins with a historic overview, followed by chapters on Clifford- and quaternion algebra and geometric (vector) differential calculus (part of Clifford analysis). The core of the book consists of one chapter on quaternion Fourier transforms and one on Clifford Fourier transforms. These core chapters and their sections on more special topics are reasonably self-contained, so that readers already somewhat familiar with quaternions and Clifford algebra will hopefully be able to begin reading directly in the chapter and section of their particular interest, without frequently needing to skip back and forth. The topics covered are of fundamental interest to pure and applied mathematicians, physicists and engineers (signal- and color image processing, electric engineering, computer science, computer graphics, artificial intelligence, geographic information science, aero-space engineering, navigation, etc.).

Features

• Intuitive real geometric approach to higher-dimensional Fourier transformations
  
• A comprehensive reference, suitable for graduate students and researchers
  
• Includes detailed definitions, properties, and many full step-by-step proofs
  
• Many figures and tables, a comprehensive biography, and a detailed index make it easy to locate information.