Although the Fourier transform is among engineering's most widely used mathematical tools, few engineers realize that the extension of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. This self-contained approach, geared toward readers with a standard background in engineering mathematics, explores the widest possible range of applications to fields such as robotics, mechanics, tomography, sensor calibration, estimation and control, liquid crystal analysis, and conformational statistics of macromolecules.
Harmonic analysis is explored in terms of particular Lie groups, and the text deals with only a limited number of proofs, focusing instead on specific applications and fundamental mathematical results. Forming a bridge between pure mathematics and the challenges of modern engineering, this updated and expanded volume offers a concrete, accessible treatment that places the general theory in the context of specific groups.
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Gregory S. Chirikjian received his PhD from the California Institute of Technology in 1992. He is Professor of Mechanical Engineering, with a secondary appointment in Computer Science, Applied Mathematics, and Statistics, at the Whiting School of Engineering at Johns Hopkins University.
Alexander B. Kyatkin received his PhD in physics from Johns Hopkins University in 1996. He has conducted research in harmonic analysis on the motion group, computer vision, numerical algorithm development, and high energy particle physics. He currently works on developing software.
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