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

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DOI: 10.4236/am.2014.56087    5,325 Downloads   6,079 Views   Citations
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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 6×3 design with 3 treatments. In our example, the underlying group is the symmetric group S3.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Zizler, P. (2014) Some Remarks on the Non-Abelian Fourier Transform in Crossover Designs in Clinical Trials. Applied Mathematics, 5, 917-927. doi: 10.4236/am.2014.56087.

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