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Exponential Sampling Series: Convergence in Mellin–Lebesgue Spaces

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Abstract

In this paper we study norm-convergence to a function f of its generalized exponential sampling series in weighted Lebesgue spaces. Key roles are taken by a result on the norm-density of the test functions and the notion of bounded coarse variation. Some examples are described.

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Acknowledgements

Carlo Bardaro and Ilaria Mantellini have been partially supported by the “Gruppo Nazionale per l’Analisi Matematica e Applicazioni (GNAMPA)” of the “Instituto di Alta Matematica (INDAM)” as well as by the projects “Ricerca di Base 2017 of University of Perugia (title: Misura, Integrazione, Approssimazione e loro Applicazioni)” and “Progetto Fondazione Cassa di Risparmio cod. nr. 2018.0419.021 (title: Metodi e Processi di Intelligenza artificiale per lo sviluppo di una banca di immagini mediche per fini diagnostici (B.I.M.))”.

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Correspondence to Carlo Bardaro.

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Dedicated to Paul Butzer, the master and friend, on the occasion of his 90th birthday, with high esteem and friendship.

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Bardaro, C., Mantellini, I. & Schmeisser, G. Exponential Sampling Series: Convergence in Mellin–Lebesgue Spaces. Results Math 74, 119 (2019). https://doi.org/10.1007/s00025-019-1044-5

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Keywords

  • Mellin–Lebesgue spaces
  • generalized exponential sampling series
  • bounded coarse variation

Mathematics Subject Classification

  • Primary 41A58
  • 42C15
  • 94A20
  • Secondary 46E22