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

作     者：Peter Zizler 

作者机构：Department of Mathematics/Physics and Engineering Mount Royal University Calgary Canada 

出 版 物：《Applied Mathematics》 (应用数学（英文）)

年 卷 期：2014年第5卷第6期

页      面：917-927页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

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

摘      要：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.