Mellin Analysis, Transform Theory, and Applications : A Self-Contained Approach / / by Carlo Bardaro, Paul L. Butzer, Ilaria Mantellini, Gerhard Schmeisser
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| Autore: |
Bardaro Carlo
|
| Titolo: |
Mellin Analysis, Transform Theory, and Applications : A Self-Contained Approach / / by Carlo Bardaro, Paul L. Butzer, Ilaria Mantellini, Gerhard Schmeisser
|
| Pubblicazione: | Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2025 |
| Edizione: | 1st ed. 2025. |
| Descrizione fisica: | 1 online resource (844 pages) |
| Disciplina: | 515.723 |
| Soggetto topico: | 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 | |
| Soggetto genere / forma: | Llibres electrònics |
| Altri autori: |
ButzerPaul L
MantelliniIlaria
SchmeisserGerhard
|
| 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. |
| Titolo autorizzato: | Mellin Analysis, Transform Theory, and Applications |
| ISBN: | 3-031-96672-4 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9911049183603321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Mathematics and Statistics Series