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

Author(s)
Peter Zizler

Affiliation(s)

Department of Mathematics/Physics and Engineering, Mount Royal University, Calgary, Canada.

Department of Mathematics/Physics and Engineering, Mount Royal University, Calgary, Canada.

Abstract

Let *G* be a non-abelian
group and let l^{2}*(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 *l*^{2}*(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 *S*_{3}.

Keywords

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

Non-Abelian Fourier Transform, Group Algebra, Irreducible Representation, Irreducible Character,

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.

Zizler, P. (2014) Some Remarks on the Non-Abelian Fourier Transform in Crossover Designs in Clinical Trials.

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