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Maslen, D. and Rockmore, D. (1997) Generalized FFTs—A Survey of Some Recent Results. In: Finkelstein, L. and Kantor, W., Eds., Proceedings of the DIMACS Workshop on Groups and Computation, 183-237.

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• TITLE: Some Remarks on the Non-Abelian Fourier Transform in Crossover Designs in Clinical Trials

  AUTHORS: Peter Zizler

  KEYWORDS: Non-Abelian Fourier Transform, Group Algebra, Irreducible Representation, Irreducible Character, G-Circulant Matrix, G-Decorrelated Decomposition, Crossover Designs in Clinical Trials

  JOURNAL NAME: Applied Mathematics, Vol.5 No.6, April 8, 2014

  ABSTRACT: Let G be a non-abelian group and let l2(G) be a finite dimensional Hilbert space of all complex valued functions for which the elements of G form the (standard) orthonormal basis. In our paper we prove results concerning G-decorrelated decompositions of functions in l2(G). These G-decorrelated decompositions are obtained using the G-convolution either by the irreducible characters of the group G or by an orthogonal projection onto the matrix entries of the irreducible representations of the group G. Applications of these G-decorrelated decompositions are given to crossover designs in clinical trials, in particular the William’s 6×3design with 3 treatments. In our example, the underlying group is the symmetric group S3.