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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. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises.” - Ken Ross, MAA Online
| Price | Condition | Delivery | Seller | Action |
| $99.99 | Digital |
| WonderClub |
Donald Holland
reviewed Classical Fourier Analysis on February 05, 2015
Classical Fourier Analysis
A good book, in which Glete first lays down the theoretical framework of his views on early modern state building: that fiscal-military states are complex organizations created by innovative rulers and they were possible because the state more and more became the most efficient protection seller within a country. Then, he examines Spain, Dutch Republic and Sweden's state building efforts according to this theory.
His ideas generally make sense and are well written, but they don't go much further than debunking myths about absolutism and explaining the steps of early modern state building. Glete doesn't really explain why most other European countries created fiscal-military organizations later than the three countries he examines. Was it because their rulers were not innovative or skilled enough? Why did Castille and Sweden succeed in curtailing their estates and setting up permanent taxation and large professional armies, while France, England or Austria couldn't (until much later)? These are relevant questions which were poorly, if at all addressed by Glete. Additionally, repetition of his theoretical formulations (like the one I summarized in the first paragraph) again and again makes the book more boring and monotonous than it could have been.
What Glete handled perfectly is the short summaries and analyses of histiography in both theoretical and case-study chapters. These really put his study in the proper context, and is very important for especially beginners in the field (like me) so that they don't take Glete's book as objective historical truth, but as a possible explanation of how (but sadly, not why) European fiscal-military states came about.
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