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Displaying similar documents to “An elementary proof of the decomposition of measures on the circle group”

On the relationships between Fourier-Stieltjes coefficients and spectra of measures

Przemysław Ohrysko, Michał Wojciechowski (2014)

Studia Mathematica

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We construct examples of uncountable compact subsets of complex numbers with the property that any Borel measure on the circle group with Fourier coefficients taking values in this set has a natural spectrum. For measures with Fourier coefficients tending to 0 we construct an open set with this property. We also give an example of a singular measure whose spectrum is contained in our set.

A characterization of the invertible measures

A. Ülger (2007)

Studia Mathematica

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Let G be a locally compact abelian group and M(G) its measure algebra. Two measures μ and λ are said to be equivalent if there exists an invertible measure ϖ such that ϖ*μ = λ. The main result of this note is the following: A measure μ is invertible iff |μ̂| ≥ ε on Ĝ for some ε > 0 and μ is equivalent to a measure λ of the form λ = a + θ, where a ∈ L¹(G) and θ ∈ M(G) is an idempotent measure.

Taylor Spectrum and Characteristic Functions of Commuting 2-Contractions

Bendoukha, Berrabah (2008)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 47A10, 47A13. In this paper, we give a description of Taylor spectrum of commuting 2-contractions in terms of characteritic functions of such contractions. The case of a single contraction obtained by B. Sz. Nagy and C. Foias is generalied in this work.

On the generalized Kato spectrum

Benharrat, Mohammed, Messirdi, Bekkai (2011)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 47A10. We show that the symmetric difference between the generalized Kato spectrum and the essential spectrum defined in [7] by sec(T) = {l О C ; R(lI-T) is not closed } is at most countable and we also give some relationship between this spectrum and the SVEP theory.