Date of Award
Mathematics and Statistics
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In this thesis, we undertake an harmonic analysis of the Banach algebra L (B) of bounded linear operators on a homogeneous Banach space B of functions on a topological abelian group G. Our analysis is divided into two major parts. In the first, we examine the case where G is compact, particularly G = T (the circle group), and in the second G is locally compact. In both cases, we define the classes of invariant and almost invariant operators in L (B) and investigate their properties. With each T ∈ L (B), we associate a Fourier series and show that this series converges to T in a certain specified sense. For G = T , we show that formal properties of the usual Fourier series hold and also obtain a generalization of the classical F. and M. Riesz theorem for B = CT . For locally compact G, we investigate a subspace of the class of almost invariant operators, namely the almost periodic operators.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2003 .E46. Source: Masters Abstracts International, Volume: 42-02, page: 0601. Adviser: Zhiguo Hu. Thesis (M.Sc.)--University of Windsor (Canada), 2003.
Emmanuel, Olusakin Joshua., "An harmonic analysis for operators on homogeneous Banach spaces." (2003). Electronic Theses and Dissertations. 1082.