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

In: Mathematical Control Theory and Finance

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jean-Paul Gauthier & Fethi Smach & Cedric Lemaître & Johel Miteran, 2008. "Finding Invariants of Group Actions on Function Spaces, a General Methodology from Non-Abelian Harmonic Analysis," Springer Books, in: Andrey Sarychev & Albert Shiryaev & Manuel Guerra & Maria do Rosário Grossinho (ed.), Mathematical Control Theory and Finance, pages 161-186, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69532-5_10
    DOI: 10.1007/978-3-540-69532-5_10
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