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Wiener's lemma
Linnaeus University, Faculty of Technology, Department of Mathematics.
2013 (English)Independent thesis Advanced level (degree of Master (Two Years)), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

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.

Place, publisher, year, edition, pages
2013.
Keyword [en]
Wiener's lemma, Banach algebra, quasi-norm, p-norm, submultiplicative weight function
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:lnu:diva-27270OAI: oai:DiVA.org:lnu-27270DiVA: diva2:634063
Supervisors
Examiners
Available from: 2013-07-01 Created: 2013-06-28 Last updated: 2013-07-01Bibliographically approved

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Department of Mathematics
Mathematical Analysis

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