In search of the invisible spectrum

DOI10.5802/aif.1743zbMath0947.46035OpenAlexW2330241241MaRDI QIDQ1807909

Nikolai Nikolski

Publication date: 24 November 1999

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1999__49_6_1925_0

zbMATH Keywords

commutative Banach algebrasmeasure algebraoperator algebrascyclic groupsformal power seriesLCA groupsfunction algebrascritical constantsBézout equationsalgebra of absolutely convergent Dirichlet seriesalgebra of almost periodic functionsbest majorantsinvisible spectrumnorm controlled inversionnorm-controlled functional calculispectral hullsWiener-Pitt-Sreider phenomenon

Mathematics Subject Classification ID

Ideals, maximal ideals, boundaries (46J20) Spectral sets of linear operators (47A25) Functional calculus in topological algebras (46H30) Measure algebras on groups, semigroups, etc. (43A10)

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Cites Work

• The functions which operate on Fourier transforms
• A corona theorem for countably many functions
• Estimates in Carleson's corona theorem and finitely generated ideals in an \(H^\infty\) algebra
• On the spectral radius formula in Banach algebras
• Boundary Values of Continuous Analytic Functions
• A Note on Constructive Methods in Banach Algebras
• Shorter Notes: A Simple Proof of Wiener's 1/f Theorem
• An Unbounded Inverse Property in the Algebra of Absolutely Convergent Fourier Series
• Sur le théorème de Beurling-Pollard.
• Les fonctions qui opèrent dans certaines algèbres à poids.
• Estimations des solutions de l'équation de Bezout dans les algèbres de Beurling analytiques
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