The Foundation of Mellin Analysis

Carlo Bardaro, Paul L. Butzer, Ilaria Mantellini and Gerhard Schmeisser
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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

Chapter Chapter 3 in Mellin Analysis, Transform Theory, and Applications, 2025, pp 51-90 from Springer

Abstract: 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.

Date: 2025
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DOI: 10.1007/978-3-031-96672-9_3

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