An Invitation to Fourier Analysis and Distribution Theory - Couverture souple

Müller, Detlef

Couverture souple

ISBN 10 : 3032315492 ISBN 13 : 9783032315496

Editeur : Springer Nature Switzerland AG, 2026

Synopsis

This book provides a rigorous introduction to Fourier analysis and the theory of distributions without presupposing an advanced background in functional analysis or measure-theoretic integration.

The guiding principle throughout is to present the material in an elementary and direct manner without sacrificing mathematical precision or depth. After introducing Fourier series and their fundamental properties in the first chapter, the main ideas of Fourier analysis are developed first for non-periodic functions on Euclidean space, where many concepts can be presented more transparently, and are subsequently transferred to the periodic setting. Likewise, distribution theory is initially developed in the framework of tempered distributions, which allows for a simpler exposition and is particularly well suited to applications in partial differential equations, including those discussed in Chapter 7. Distributions on open subsets of Euclidean space are then introduced via localization, emphasizing their inherently local character. The final chapter presents an elementary proof of the Schwartz kernel theorem based on expansions in Hermite functions, from which the tensor product of distributions is obtained as an immediate consequence. Each chapter concludes with a collection of exercises ranging from routine applications to more challenging problems.

Détails de l'édition

• Éditeur: Springer Nature Switzerland AG
• Date d'édition: 2026
• Langue: anglais
• ISBN 10: 3032315492
• ISBN 13: 9783032315496
• Reliure: Broché
• Nombre de pages: 212
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne