The Mellin Transform in Spaces X c p $$X_c^p$$ for 1

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 7 in Mellin Analysis, Transform Theory, and Applications, 2025, pp 201-215 from Springer

Abstract: Abstract In this chapter, we first define the Mellin transform in the Hilbert spaceSpaceHilbert X c 2 $$X_c^2$$ . Then, using the Riesz–Thorin interpolation theoremTheoremRiesz–Thorin (Theorem 1.22 ), we extend the definition to the spaces X c p $$X^p_c$$ for 1 2 $$p>2$$ can be treated within the theory of distributions. However, we will not cover this topic in the present book but give a brief outline in the notes.

Date: 2025
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DOI: 10.1007/978-3-031-96672-9_7

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