Výzkum
	Kolokvia

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 either obtained using the G-convolution 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.