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Wiener's lemma

In this thesis we study Wiener’s lemma. The classical version of the lemma, whose realm is a Banach algebra, asserts that the pointwise inverse of a nonzero function with absolutely convergent Fourier expansion, also possesses an absolutely convergent Fourier expansion. The main purpose of this thesis is to investigate the validity inalgebras endowed with a quasi-norm or a p-norm.As a warmup, we prove the classical version of Wiener’s lemma using elemen-tary analysis. Furthermore, we establish results in Banach algebras concerning spectral theory, maximal ideals and multiplicative linear functionals and present a proof Wiener’s lemma using Banach algebra techniques. Let ν be a submultiplicative weight function satisfying the Gelfand-Raikov-Shilov condition. We show that if a nonzero function f has a ν-weighted absolutely convergent Fourier series in a p-normed algebra A. Then 1/f also has a ν-weightedabsolutely convergent Fourier series in A.

Identiferoai:union.ndltd.org:UPSALLA1/oai:DiVA.org:lnu-27270
Date January 2013
CreatorsFredriksson, Henrik
PublisherLinnéuniversitetet, Institutionen för matematik (MA)
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeStudent thesis, info:eu-repo/semantics/bachelorThesis, text
Formatapplication/pdf
Rightsinfo:eu-repo/semantics/openAccess

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