Overview
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.
Full Product Details
Author: Loukas Grafakos
Publisher: Springer-Verlag New York Inc.
Imprint: Springer-Verlag New York Inc.
Edition: Softcover reprint of hardcover 2nd ed. 2009
Volume: 250
Dimensions:
Width: 15.50cm
, Height: 2.60cm
, Length: 23.50cm
Weight: 0.795kg
ISBN: 9781441918567
ISBN 10: 1441918566
Pages: 507
Publication Date: 19 November 2010
Audience:
Professional and scholarly
,
Professional & Vocational
Replaced By: 9781493912292
Format: Paperback
Publisher's Status: Active
Availability: Out of print, replaced by POD
We will order this item for you from a manufatured on demand supplier.
Reviews
From a reviews: 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 From the reviews of the second edition: The author ! has produced a very well-written, polished, and exciting graduate textbook which easily doubles as a reference book in a number of areas belonging to or touching on Fourier analysis. ! 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'. ! I think it's nigh-on indispensable for the aspiring Fourier analyst. (Michael Berg, MAA Online, January, 2009) The second part of the two volume treatise in harmonic analysis entitled 'Modern Fourier Analysis' is designed to be a continuation of the first volume ! . The historical notes in each chapter are intended to provide an account of past research as well as to suggest directions for further investigation. The volume is mainly addressed to graduate students who wish to study harmonic analysis. (Leonid Golinskii, Zentralblatt MATH, Vol. 1158, 2009) Intended for graduate students who wish to study Fourier analysis. ! also suitable for self-study. Proofs are provided in great detail. Each chapter is followed by historical notes with references, often including a discussion of further results. There are numerous exercises of varying difficulty, with hints and references provided for the harder ones. ! certainly a valuable and useful addition to the existing literature and can serve as textbooks or as reference books. Students will especially appreciate the extensive collection of exercises. (Andreas Seeger, Mathematical Reviews, Issue 2011 d)
From a reviews: 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 From the reviews of the second edition: The author ... has produced a very well-written, polished, and exciting graduate textbook which easily doubles as a reference book in a number of areas belonging to or touching on Fourier analysis. ... 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,. ... I think it,s nigh-on indispensable for the aspiring Fourier analyst. (Michael Berg, MAA Online, January, 2009) The second part of the two volume treatise in harmonic analysis entitled 'Modern Fourier Analysis, is designed to be a continuation of the first volume ... . The historical notes in each chapter are intended to provide an account of past research as well as to suggest directions for further investigation. The volume is mainly addressed to graduate students who wish to study harmonic analysis. (Leonid Golinskii, Zentralblatt MATH, Vol. 1158, 2009) Intended for graduate students who wish to study Fourier analysis. ... also suitable for self-study. Proofs are provided in great detail. Each chapter is followed by historical notes with references, often including a discussion of further results. There are numerous exercises of varying difficulty, with hints and references provided for the harder ones. ... certainly a valuable and useful addition to the existing literature and can serve as textbooks or as reference books. Students will especially appreciate the extensive collection of exercises. (Andreas Seeger, Mathematical Reviews, Issue 2011 d)
From a reviews: 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 From the reviews of the second edition: The author ! has produced a very well-written, polished, and exciting graduate textbook which easily doubles as a reference book in a number of areas belonging to or touching on Fourier analysis. ! 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'. ! I think it's nigh-on indispensable for the aspiring Fourier analyst. (Michael Berg, MAA Online, January, 2009) The second part of the two volume treatise in harmonic analysis entitled 'Modern Fourier Analysis' is designed to be a continuation of the first volume ! . The historical notes in each chapter are intended to provide an account of past research as well as to suggest directions for further investigation. The volume is mainly addressed to graduate students who wish to study harmonic analysis. (Leonid Golinskii, Zentralblatt MATH, Vol. 1158, 2009)
From a reviews: ""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 From the reviews of the second edition: ""The author ... has produced a very well-written, polished, and exciting graduate textbook which easily doubles as a reference book in a number of areas belonging to or touching on Fourier analysis. ... 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,. ... I think it,s nigh-on indispensable for the aspiring Fourier analyst."" (Michael Berg, MAA Online, January, 2009) ""The second part of the two volume treatise in harmonic analysis entitled 'Modern Fourier Analysis, is designed to be a continuation of the first volume ... . The historical notes in each chapter are intended to provide an account of past research as well as to suggest directions for further investigation. The volume is mainly addressed to graduate students who wish to study harmonic analysis."" (Leonid Golinskii, Zentralblatt MATH, Vol. 1158, 2009) ""Intended for graduate students who wish to study Fourier analysis. ... also suitable for self-study. Proofs are provided in great detail. Each chapter is followed by historical notes with references, often including a discussion of further results. There are numerous exercises of varying difficulty, with hints and references provided for the harder ones. ... certainly a valuable and useful addition to the existing literature and can serve as textbooks or as reference books. Students will especially appreciate the extensive collection of exercises."" (Andreas Seeger, Mathematical Reviews, Issue 2011 d)
From a reviews: 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 From the reviews of the second edition: The author ... has produced a very well-written, polished, and exciting graduate textbook which easily doubles as a reference book in a number of areas belonging to or touching on Fourier analysis. ... 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'. ... I think it's nigh-on indispensable for the aspiring Fourier analyst. (Michael Berg, MAA Online, January, 2009) The second part of the two volume treatise in harmonic analysis entitled 'Modern Fourier Analysis' is designed to be a continuation of the first volume ... . The historical notes in each chapter are intended to provide an account of past research as well as to suggest directions for further investigation. The volume is mainly addressed to graduate students who wish to study harmonic analysis. (Leonid Golinskii, Zentralblatt MATH, Vol. 1158, 2009) Intended for graduate students who wish to study Fourier analysis. ... also suitable for self-study. Proofs are provided in great detail. Each chapter is followed by historical notes with references, often including a discussion of further results. There are numerous exercises of varying difficulty, with hints and references provided for the harder ones. ... certainly a valuable and useful addition to the existing literature and can serve as textbooks or as reference books. Students will especially appreciate the extensive collection of exercises. (Andreas Seeger, Mathematical Reviews, Issue 2011 d)
