1.

Record Nr.

UNINA9911049183603321

Autore

Bardaro Carlo

Titolo

Mellin Analysis, Transform Theory, and Applications : A Self-Contained Approach / / by Carlo Bardaro, Paul L. Butzer, Ilaria Mantellini, Gerhard Schmeisser

Pubbl/distr/stampa

Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2025

ISBN

3-031-96672-4

Edizione

[1st ed. 2025.]

Descrizione fisica

1 online resource (844 pages)

Collana

Mathematics and Statistics Series

Altri autori (Persone)

ButzerPaul L

MantelliniIlaria

SchmeisserGerhard

Disciplina

515.723

Soggetti

Fourier analysis

Functions of complex variables

Functions, Special

Functional analysis

Fourier Analysis

Functions of a Complex Variable

Special Functions

Functional Analysis

Anàlisi funcional

Anàlisi de Fourier

Funcions de variables complexes

Funcions especials

Llibres electrònics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

- 1. Preliminaries -- 2. Polar-Analytic Functions -- 3. The Foundation of Mellin Analysis -- 4. The Mellin Convolution -- 5. The Finite Mellin transform and the Mellin–Fourier Series -- 6. The Mellin Transform in Xc -- 7. The Mellin Transform in Spaces Xp/c for 1 < p ≤ 2 -- 8. Mellin Bandlimited Functions and Paley–Wiener Theorems in Mellin Setting -- 9. Mellin Transforms and Fractional Analysis -- 10. The Mellin Distance -- 11. Mellin Transform Methods for Partial Differential Equations --



12. Exponential Sampling Theory -- 13. Generalized Exponential Sampling Theory -- 14. Applications to Quadrature over the Positive Real Axis.

Sommario/riassunto

This monograph presents the theory of the Mellin transform and the resulting Mellin analysis in a rigorous and unified manner. Often dismissed as a subordinate topic within Fourier and Laplace transform, it is instead demonstrated here that the theory is completely independent, can be studied within a self-contained framework, and exhibits some typical characteristics. In addition to highlighting the foundations of the theory, the book addresses applications to certain partial differential equations, sampling theory and numerical quadrature. These applications provide methods which are in turn of interest in various areas of mathematics, science, and engineering. Each chapter is enriched by numerous references to further literature and potential research directions. Researchers working in this field will gain new insights and appreciate the deserved attention for this underrated topic in harmonic analysis.