Results in Mathematics

, 74:119 | Cite as

Exponential Sampling Series: Convergence in Mellin–Lebesgue Spaces

  • Carlo BardaroEmail author
  • Ilaria Mantellini
  • Gerhard Schmeisser


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.


Mellin–Lebesgue spaces generalized exponential sampling series bounded coarse variation 

Mathematics Subject Classification

Primary 41A58 42C15 94A20 Secondary 46E22 



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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer SciencesUniversity of PerugiaPerugiaItaly
  2. 2.Department MathematikFriedrich-Alexander Universität Erlangen-NürnbergErlangenGermany

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