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On Idempotent Measures of Small Norm

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thesis
posted on 15.11.2021, 17:04 by Mudge, Jayden

In 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

01/01/2016

Date of Award

01/01/2016

Publisher

Te Herenga Waka—Victoria University of Wellington

Rights License

Author Retains Copyright

Degree Discipline

Mathematics

Degree Grantor

Te Herenga Waka—Victoria University of Wellington

Degree Level

Masters

Degree Name

Master of Science

ANZSRC Type Of Activity code

970101 Expanding Knowledge in the Mathematical Sciences

Victoria University of Wellington Item Type

Awarded Research Masters Thesis

Language

en_NZ

Victoria University of Wellington School

School of Mathematics, Statistics and Operations Research

Advisors

Pham, Hung