Description

This book discusses, develops and applies the theory of Vilenkin-Fourier series connected to modern harmonic analysis. The classical theory of Fourier series deals with decomposition of a function into sinusoidal waves. This book discusses, develops and applies the theory of Vilenkin-Fourier series connected to modern harmonic analysis. The classical theory of Fourier series deals with decomposition of a function into sinusoidal waves. Unlike these continuous waves the Vilenkin (Walsh) functions are rectangular waves. Such waves have already been used frequently in the theory of signal transmission, multiplexing, filtering, image enhancement, code theory, digital signal processing and pattern recognition. The development of the theory of Vilenkin-Fourier series has been strongly influenced by the classical theory of trigonometric series. Because of this it is inevitable to compare results of Vilenkin-Fourier series to those on trigonometric series. There are many similarities between these theories, but there exist differences also. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group. The first part of the book can be used as an introduction to the subject, and the following chapters summarize the most recent research in this fascinating area and can be read independently. Each chapter concludes with historical remarks and open questions. The book will appeal to researchers working in Fourier and more broad harmonic analysis and will inspire them for their own and their students’ research. Moreover, researchers in applied fields will appreciate it as a sourcebook far beyond the traditional mathematical domains.

Langue

en

Version

Couverture rigide

Date de sortie initiale

23 novembre 2022

Nombre de pages

626

Illustrations

Avec illustrations

Personnes impliquées

Auteur principal

Lars-Erik Persson

Deuxième auteur

George Tephnadze

Editeur principal

Birkhauser Verlag Ag

Informations sur le fabricant

Nom du fabricant

Springer Nature Customer Service Center GmbH

Adresse du fabricant

Europaplatz 3 | 69115| Heidelberg| DE

Adresse électronique du fabricant

ProductSafety@springernature.com

Informations sur le fabricant

Les informations du fabricant ne sont actuellement pas disponibles

Autres spécifications

Hauteur de l’emballage

235 mm

Largeur d’emballage

155 mm

Largeur du produit

155 mm

Livre d‘étude

Non

Longueur d’emballage

235 mm

Longueur du produit

235 mm

Poids de l’emballage

1124 g

Édition

1st ed. 2022

EAN

EAN

9783031144585

Sécurité des produits

Opérateur économique responsable dans l’UE

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Catégories

Science et nature

Mathématiques

Calcul et analyse mathématique

Analyse complexe

Calcul fonctionnel

Livres

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Livre

Disponibilité

Disponible à l’adresse suivante

Langue

Anglais

Type de livre

Hardcover