NDLI: An operational calculus for the euclidean motion group with applications in robotics and polymer science

Content Provider	Springer Nature Link
Author	Chirikjian, Gregory S. Kyatkin, Alexander B.
Copyright Year	2000
Abstract	In this article we develop analytical and computational tools arising from harmonic analysis on the motion group of three-dimensional Euclidean space. We demonstrate these tools in the context of applications in robotics and polymer science. To this end, we review the theory of unitary representations of the motion group of three dimensional Euclidean space. The matrix elements of the irreducible unitary representations are calculated and the Fourier transform of functions on the motion group is defined. New symmetry and operational properties of the Fourier transform are derived. A technique for the solution of convolution equations arising in robotics is presented and the corresponding regularized problem is solved explicity for particular functions. A partial differential equation from polymer science is shown to be solvable using the operational properties of the Euclidean-group Fourier transform.
Starting Page	583
Ending Page	606
Page Count	24
File Format	PDF
ISSN	10695869
Journal	Journal of Fourier Analysis and Applications
Volume Number	6
Issue Number	6
e-ISSN	15315851
Language	English
Publisher	Birkhäuser-Verlag
Publisher Date	2000-01-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	convolution Euclidean group rigid body motion diffusion equations inverse problems regularization Fourier transform harmonic analysis Abstract Harmonic Analysis Approximations and Expansions Fourier Analysis Partial Differential Equations Applications of Mathematics Signal, Image and Speech Processing
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

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An operational calculus for the euclidean motion group with applications in robotics and polymer science

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