The Finite Mellin Transform and the Mellin–Fourier Series

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 5 in Mellin Analysis, Transform Theory, and Applications, 2025, pp 101-123 from Springer

Abstract: Abstract In this chapter, we first introduce the finite Mellin transform of functions in Y c $$ Y_c$$ and present its basic properties. Then we consider an inversion of this transform which leads us to Mellin–Fourier series. After establishing approximations by partial sums represented by finite Mellin convolutions with appropriate kernels, we study convergence of Mellin–Fourier series in the spaces Y c $$Y_c$$ and Y c 2 $$Y_c^2$$ .

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-96672-9_5

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DOI: 10.1007/978-3-031-96672-9_5

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