| Engineering
Applications of Noncommutative Harmonic Analysis: With Emphasis
on Rotation and Motion Groups
| Gregory
S Chirikjian |
|
Johns
Hopkins University, Baltimore, Maryland, USA |
| Alexander
B Kyatkin |
|
|
|
| |
- Provides
a bridge between pure mathematics and the challenges of modern
engineering
- Explores
a broad range of applications, including robotics, mechanics,
tomography, sensor calibration, estimation and control, liquid
crystal analysis, and conformational statistics of macromolecules
- Offers
a comprehensive review of classical Fourier analysis, orthogonal
functions, wavelets, and fast Fourier transforms
- Presents
the general theory in the context of particular groups, resulting
in a concrete treatment accessible to engineers
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. |
