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This book is intended to present the selected topics in depth and stimulate further study. The primary goal of this book is to present the theoretical foundation of the field of Euclidean Harmonic analysis. There are numerous exercises of varying difficulty, with hints and references provided for the harder ones. 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.
The prerequisites are satisfactory completion of courses in real and complex variables, and knowledge of classical Fourier analysis topics.
Chapters in modefn 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.
Modern Fourier Analysis: Preliminary Entry – Loukas Grafakos – Bok () | Bokus
fourifr 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. It is designed to be a continuation of the rst v- ume. Modern Fourier Analysis Loukas Grafakos. Proofs are provided in great detail. Smoothness and Function Spaces. The new chapter will tie foufier with the material in chapters 8, 9, and 10, and the author may add a new section in this chapter applying the techniques of chapter 11 in the context of multilinear harmonic analysis.
Appendix A The Schur Lemma. Students will especially appreciate the extensive collection fouriwr exercises. Modern Fourier Analysis sports a huge number off well-designed problems and exercises, and every chapter ends with an exceedingly informative set of ‘Historical Notes’.
It is more suitable for readers who want to get a feel for current research. Appendix B Smoothness and Vanishing Moments. Bloggat om Modern Fourier Analysis: These theorems are proved in great detail and their proofs are organized to present the ow of ideas. Moreover, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises.
The historical notes in each chapter are intended to provide an account of past research as well as modetn suggest directions for further investigation.
Modern Fourier Analysis: Preliminary Entry 250
Analgsis treatment is thoroughly modern with free use of operators and functional analysis. Liquid Mark A Miodownik Inbunden. Contents 1 Smoothness and Function Spaces.
IamdelightedthatSpringerhasofferedtopublish the second edition of this book in two volumes: Grafamos Fourier Analysis Loukas Grafakos. SpringerNov 13, – Mathematics – pages. The historical notes in each chapter are intended to provide an account of past research but also to suggest directions for further investigation. Selected pages Title Page.
Preliminary Entry av Loukas Grafakos. In addition to a new chapter, the third edition contains different corrections and improvements in the existing text, more geafakos and applications, new and more relevant hints for the existing exercises, about new exercises in the existing chapters, and improved references.
Each chapter is followed by historical notes with references, often including a discussion of further results. Account Options Sign in. I think it’s nigh-on indispensable for the aspiring Fourier analyst. My library Help Advanced Book Search.
The volume is mainly addressed to graduate students who wish to study harmonic analysis. This second volume is intended to serve as annalysis text for a seco- semester course in the subject. This book is mainly addressed to graduate students in mathematics. This book is Modern in that is contains more recent topics such as function spaces, atomic decompositions, singular integrals of nonconvolution type, and weighted inequalities.
These volumes are mainly addressed to graduate students who wish to study Fourier analysis.