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On Idempotent Measures of Small Norm
thesis
posted on 2021-11-15, 17:04 authored by Mudge, JaydenIn this Master’s Thesis, we set up the groundwork for [8], a paper co-written by the author and Hung Pham. We summarise the Fourier and Fourier-Stieltjes algebras on both abelian and general locally compact groups. Let Г be a locally compact group. We answer two questions left open in [11] and [13]: 1. When Г is abelian, we prove that if ϰs ∈ B(Г) is an idempotent with norm 1 < ||ϰs|| < 4/3 then S is the union of two cosets of an open subgroup of Г. 2. For general Г, we prove that if ϰs ∈ McbA(Г) is an idempotent with norm ||ϰs||cb < 1+√2/2 , then S is an open coset in Г.
History
Copyright Date
2016-01-01Date of Award
2016-01-01Publisher
Te Herenga Waka—Victoria University of WellingtonRights License
Author Retains CopyrightDegree Discipline
MathematicsDegree Grantor
Te Herenga Waka—Victoria University of WellingtonDegree Level
MastersDegree Name
Master of ScienceANZSRC Type Of Activity code
970101 Expanding Knowledge in the Mathematical SciencesVictoria University of Wellington Item Type
Awarded Research Masters ThesisLanguage
en_NZVictoria University of Wellington School
School of Mathematics, Statistics and Operations ResearchAdvisors
Pham, HungUsage metrics
Keywords
Fourier analysisMeasure theoryGroup algebrasSchool: School of Mathematics, Statistics and Operations Research010108 Operator Algebras and Functional Analysis970101 Expanding Knowledge in the Mathematical SciencesDegree Discipline: MathematicsDegree Level: MastersDegree Name: Master of ScienceOperator Algebras and Functional Analysis
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