Finding Invariants of Group Actions on Function Spaces, a General Methodology from Non-Abelian Harmonic Analysis

Jean-Paul Gauthier (), Fethi Smach (), Cedric Lemaître () and Johel Miteran ()
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Jean-Paul Gauthier: Université de Bourgogne, LE2I, UMR CNRS 5158
Fethi Smach: Université de Bourgogne, LE2I, UMR CNRS 5158
Cedric Lemaître: Université de Bourgogne, LE2I, UMR CNRS 5158
Johel Miteran: Université de Bourgogne, LE2I, UMR CNRS 5158

A chapter in Mathematical Control Theory and Finance, 2008, pp 161-186 from Springer

Abstract: Summary In this paper, we describe a general method using the abstract non-Abelian Fourier transform to construct “rich” invariants of group actions on functional spaces. In fact, this method is inspired of a classical method from image analysis: the method of Fourier descriptors, for discrimination among “contours” of objects. This is the case of the Abelian circle group, but the method can be extended to general non-Abelian cases. Here, we improve on some of our previous developments on this subject, in particular in the case of compact groups and motion groups. The last point (motion groups) is in the perspective of invariant image analysis. But our method can be applied to many practical problems of discrimination, or detection, or recognition.

Keywords: Compact Group; Haar Measure; Motion Group; Unitary Irreducible Representation; Fourier Descriptor (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-69532-5_10

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DOI: 10.1007/978-3-540-69532-5_10

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