Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis on Rotation and Motion Groups, 1st Edition (Hardback) book cover

Engineering Applications of Noncommutative Harmonic Analysis

With Emphasis on Rotation and Motion Groups, 1st Edition

By Gregory S. Chirikjian, Alexander B. Kyatkin

CRC Press

674 pages

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Hardback: 9780367257187
pub: 2019-06-06
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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.

Reviews

"In the opinion of this reviewer, the authors have accomplished their stated aims. [The book] is a comprehensive and generally self-contained exposition appropriate for guiding the engineering student to familiarity and, with practice, perhaps competence in an elegant and useful branch of analysis…it must certainly be considered as a solid reference addition to personal or institutional libraries. This reviewer welcomes it in his"

- Appl Mech Rev, Vol. 55, no. 1, January 2002

"There is a substantial list of over 310 references…Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis on Rotation and Motion Groups should be a source of enlightenment to the reader on many hitherto unexplored issues and concepts connecting the production and dissipation ranges of turbulence and the unstable developmental phases leading to these states. The authors have succeeded in producing a very readable and informative book that should act to stimulate additional discussions…It is recommended for research laboratory and academic library acquisition as a novel source of important developments."

-Appl Mech Rev, vol. 54, no.6, November 2001

"This book is an extensive account of the engineering applications of noncommutative harmonic analysis, that is, Fourier analysis on noncummutative Lie groups…The presentation throughout the book is explicit and highly computational. In addition, each chapter is supplemented with extensive references to the literature, both engineering and mathematical…Mathematicians will find the book interesting as a source of mathematical problems awaiting resolution, particularly those related to fast algorithms for the computation of the integrals involved"

-David H. Sattinger, Utah State University

" …comprehensible and self-contained…a valuable fuide to the literature, both engineering and mathematical. ….Although the book is intended primarily for engineers, it is also interesting for mathematicians as a source of mathematical problems."

- Mathematical Reviews, 2003g

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

About the Authors

Gregory S. Chirikjian and Alexander B. Kyatkin.

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Subject Categories

BISAC Subject Codes/Headings:
COM059000
COMPUTERS / Computer Engineering
MAT003000
MATHEMATICS / Applied
TEC009070
TECHNOLOGY & ENGINEERING / Mechanical