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Mellin analysis and its basic associated metric—applications to sampling theory

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Abstract

In this paper a notion of functional “distance” in the Mellin transform setting is introduced and a general representation formula is obtained for it. Also, a determination of the distance is given in terms of Lipschitz classes and Mellin–Sobolev spaces. Finally applications to approximate versions of certain basic relations valid for Mellin band-limited functions are studied in details.

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Authors and Affiliations

  1. Department of Mathematics and Computer Sciences, University of Perugia, Perugia, Italy

    C. Bardaro & I. Mantellini

  2. Lehrstuhl A fuer Mathematik, RWTH Aachen, D-52056, Aachen, Germany

    P. L. Butzer

  3. Department of Mathematics, FAU Erlangen-Nuremberg, D-91058, Erlangen, Germany

    G. Schmeisser

Authors
  1. C. Bardaro
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  2. P. L. Butzer
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  3. I. Mantellini
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  4. G. Schmeisser
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Corresponding author

Correspondence to G. Schmeisser.

Additional information

Carlo Bardaro and Ilaria Mantellini have been partially supported by the “Gruppo Nazionale per l’Analisi Matematica e Applicazioni (GNAMPA) of the “Istituto Nazionale di Alta Matematica” (INDAM) as well as by the Department of Mathematics and Computer Sciences of the University of Perugia.

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Bardaro, C., Butzer, P.L., Mantellini, I. et al. Mellin analysis and its basic associated metric—applications to sampling theory. Anal Math 42, 297–321 (2016). https://doi.org/10.1007/s10476-016-0401-9

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  • DOI: https://doi.org/10.1007/s10476-016-0401-9

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