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

• 作者: Peter Zizler
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Non-Abelian Fourier Transform Group Algebra IRREDUCIBLE Representation IRREDUCIBLE Character G-Circulant Matrix G-Decorrelated Decomposition CROSSOVER Designs in Clinical Trials
• 年，卷（期）: 2014,（6）
• 页码范围: 917-927
• 页数: 11页
• 分类号: O1

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.