An abstract form of a theorem of Helson and applications to sets of synthesis and sets of uniqueness

DOI10.1016/j.jfa.2009.09.021zbMath1182.43006OpenAlexW2014565855MaRDI QIDQ1048192

Ali Ülger

Publication date: 11 January 2010

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2009.09.021

zbMATH Keywords

group algebramultipliersweakly almost periodic functionset of uniquenessArens productHelson setset of synthesisweak sequential compactnessweak conditional compactness

Mathematics Subject Classification ID

Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) (43A46) Spectral synthesis on groups, semigroups, etc. (43A45)

Cites Work

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• The point spectrum of weakly almost periodic functions
• The spectral characterization of a class of almost periodic functions
• A new type of sets of uniqueness
• Continuous manifolds in \(R^ n \)that are sets of interpolation for the Fourier algebra
• Geometry of Banach spaces. Selected topics
• When is the range of a multiplier on a Banach algebra closed?
• Some results on Kronecker, Dirichlet and Helson sets
• Spectral synthesis for the Kronecker sets
• Helson sets in compact and locally compact groups
• On the union of two Helson sets
• Harmonic synthesis for subgroups
• Un théorème sur les fonctions bornees et uniformement continues sur l'axe réel
• Weakly almost periodic functionals on the Fourier algebra
• Fourier transforms on perfect sets
• The Spectral Theory of Bounded Functions
• Fourier-Stieltjes transforms of measures on independent sets
• A Helson set of uniqueness but not of synthesis
• Helson Sets which Disobey Spectral Synthesis
• Examples in Helson sets
• Some Results of Narrow Spectral Analysis.
• L'algèbre de Fourier d'un groupe localement compact
• Sur les réarrangements de fonctions de la classe A
• On Narrow Spectral Analysis.
• Shorter Notes: Elementary Proof of a Theorem of Helson
• Sidon sets in $\mathsf{R}^n$.
• Drury's lemma and Helson sets
• A Characterization of SH-Sets
• The second duals of Beurling algebras
• Abstract Ergodic Theorems and Weak Almost Periodic Functions