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Acta Mathematica Hungarica

, Volume 159, Issue 1, pp 42–54 | Cite as

\(\mathcal{J}_H\)-Regular Borel measures on locally compact abelian groups

  • L. Klotz
  • J.M. MedinaEmail author
Article

Abstract

Let G be an LCA group, H a closed subgroup, \(\varGamma\) the dual group of G. In accordance with analogous notions in prediction theory the classes of \(\mathcal{J}_H\)-regular and \(\mathcal{J}_H\)-singular Borel measures on \({\rm \Gamma}\) are defined. A characterization of \(\mathcal{J}_H\)-regular measures is given and a Wold type decomposition is obtained. Relations to the Whittaker–Shannon–Kotel’nikov theorem are discussed.

Key words and phrases

LCA group regular measure \(L^{\alpha}\)-space trigonometric approximation Whittaker–Shannon–Kotel’nikov theorem 

Mathematics Subject Classification

43A15 42A10 43A05 43A25 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Fakultät für Mathematik und InformatikUniversität LeipzigLeipzigGermany
  2. 2.Departamento de MatemáticaInst. Argentino de Matemática “A. P. Calderón” – CONICET, and Universidad de Buenos AiresBuenos AiresArgentina

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