Engineering Applications of Noncommutative Harmonic Analysis : With Emphasis on Rotation and Motion Groups

著者名：Chirikjian, Gregory S./Kyatkin, Alexander B.

CRC Press（2021/02/25発売）

• 言語：ENG
• ISBN：9780367257187
• eISBN：9781000697339

Description

First published in 2001. The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems.

Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications.

Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.

Table of Contents

Introduction and Overview of Applications
Classical Fourier Analysis
Sturm-Liouville Expansions, Discrete Polynomial Transforms, and Wavelets
Orthogonal Expansions in Curvilinear Coordinates
Rotations in Three Dimensions
Rigid-Body Motion
Group Theory
Harmonic Analysis on Groups
Representation Theory and Operational Calculus for SU(2) and SO(3)
Harmonic Analysis on the Euclidean Motion Groups
Fast Fourier Transforms for Motion Groups
Robotics
Image Analysis and Tomography
Statistical Pose Determination and Camera Calibration
Stochastic Processes, Estimation, and Control
Rotational Brownian Motion and Diffusion
Statistical Mechanics of Macromolecules
Mechanics and Texture Analysis
Appendices:
Computational Complexity, Matrices, and Polynomials
Set Theory
Vector Spaces and Algebras
Matrices
Techniques from Mathematical Physics
Variational Calculus
Manifolds and Riemannian Metrics