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The Foundation of Mellin Analysis

In: Mellin Analysis, Transform Theory, and Applications

Author

Listed:
  • Carlo Bardaro

    (University of Perugia, Department of Mathematics and Informatics)

  • Paul L. Butzer

    (RWTH Aachen University, Lehrstuhl A für Mathematik)

  • Ilaria Mantellini

    (University of Perugia, Department of Mathematics and Informatics)

  • Gerhard Schmeisser

    (Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Department Mathematik)

Abstract

In this chapter we introduce the notion of the Mellin differential operator. It is based on the notion of Mellin translation which represents the Mellin counterpart of the classical translation operator T h $$\mathcal {T}_h$$ defined by T h f ( x ) = f ( x + h ) . $$\mathcal {T}_hf(x) = f(x+h).$$ We begin a section about the basic theory of the spaces on which Mellin analysis is built.

Suggested Citation

  • Carlo Bardaro & Paul L. Butzer & Ilaria Mantellini & Gerhard Schmeisser, 2025. "The Foundation of Mellin Analysis," Springer Books, in: Mellin Analysis, Transform Theory, and Applications, chapter 0, pages 51-90, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-96672-9_3
    DOI: 10.1007/978-3-031-96672-9_3
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