Modern Fourier Analysis

Loukas Grafakos

ISBN 10: 1441918566 / ISBN 13: 9781441918567

Edité par Springer New York, Springer US, 2010

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. This book is mainly addressed to graduate students in mathematics and is designed to serve for a three-course sequence on the subject. The only prerequisite for understanding the text is satisfactory completion of a course in measure theory, Lebesgue integration, and complex variables. This book is intended to present the selected topics in some depth and stimulate further study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of analysis on the torus. This material is included for historical reasons, as the genesis of Fourier analysis can be found in trigonometric expansions of periodic functions in several variables.While the 1st edition was published as a single volume, the new edition will contain 120 pp of new material, with an additional chapter on time-frequency analysis and other modern topics. As a result, the book is now being published in 2 separate volumes, the first volume containing the classical topics (Lp Spaces, Littlewood-Paley Theory, Smoothness, etc.), the second volume containing the modern topics (weighted inequalities, wavelets, atomic decomposition, etc.).From a review of the first edition:Grafakos s book is very user-friendly with numerous examples illustrating the definitions and ideas. It is more suitable for readers who want to get a feel for current research. The treatment is thoroughly modern with free use of operators and functional analysis. Moreover, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises. - Ken Ross, MAA Online.

N° de réf. du vendeur 9781441918567

Détails bibliographiques

• Titre: Modern Fourier Analysis
• Éditeur: Springer New York, Springer US
• Date de parution: 2010
• Langue: anglais
• ISBN à 10 chiffres: 1441918566
• ISBN à 13 chiffres: 9781441918567
• Reliure: Taschenbuch
• Édition: 2ème Édition
• État de l'article: Neu
• Dimensions: 235 L x 155 H x 29 P (en millimètres) 235 millimètres de largeur par 155 millimètres de hauteur par 29 millimètres de profondeur
• Poids: 785 grammes

A propos de ce titre

Synopsis

The great response to the publication of the book Classical and Modern Fourier Analysishasbeenverygratifying.IamdelightedthatSpringerhasofferedtopublish the second edition of this book in two volumes: Classical Fourier Analysis, 2nd Edition, and Modern Fourier Analysis, 2nd Edition. These volumes are mainly addressed to graduate students who wish to study Fourier analysis. This second volume is intended to serve as a text for a seco- semester course in the subject. It is designed to be a continuation of the rst v- ume. Chapters 1–5 in the rst volume contain Lebesgue spaces, Lorentz spaces and interpolation, maximal functions, Fourier transforms and distributions, an introd- tion to Fourier analysis on the n-torus, singular integrals of convolution type, and Littlewood–Paley theory. Armed with the knowledgeof this material, in this volume,the reader encounters more advanced topics in Fourier analysis whose development has led to important theorems. These theorems are proved in great detail and their proofs are organized to present the ow of ideas. The exercises at the end of each section enrich the material of the corresponding section and provide an opportunity to develop ad- tional intuition and deeper comprehension. The historical notes in each chapter are intended to provide an account of past research but also to suggest directions for further investigation. The auxiliary results referred to the appendix can be located in the rst volume.

Présentation de l'éditeur

The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. There are historical notes at the end of each chapter, and examples illustrate the definitions and ideas.