"An harmonic analysis for operators on homogeneous Banach spaces." by Olusakin Joshua. Emmanuel

Date of Award

2003

Publication Type

Master Thesis

Degree Name

M.Sc.

Department

Mathematics and Statistics

Keywords

Mathematics.

Supervisor

Hu, H.

Rights

info:eu-repo/semantics/openAccess

Abstract

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.

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