Download PDF Modern Fourier Analysis (Graduate Texts in Mathematics)

Download PDF Modern Fourier Analysis (Graduate Texts in Mathematics)

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Modern Fourier Analysis (Graduate Texts in Mathematics)

Download PDF Modern Fourier Analysis (Graduate Texts in Mathematics)

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Review

“The most up-to-date account of the most important developments in the area. … It has to be pointed out that the hard ones usually come with a good hint, which makes the book suitable for self-study, especially for more motivated students. That being said, the book provides a good reference point for seasoned researchers as well.” (Atanas G. Stefanov, Mathematical Reviews, August, 2015)

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From the Back Cover

This text is addressed to graduate students in mathematics and to interested researchers who wish to acquire an in depth understanding of Euclidean Harmonic analysis. The text covers modern topics and techniques in function spaces, atomic decompositions, singular integrals of nonconvolution type, and the boundedness and convergence of Fourier series and integrals. The exposition and style are designed to stimulate further study and promote research. Historical information and references are included at the end of each chapter.This third edition includes a new chapter entitled "Multilinear Harmonic Analysis" which focuses on topics related to multilinear operators and their applications. Sections 1.1 and 1.2 are also new in this edition. Numerous corrections have been made to the text from the previous editions and several improvements have been incorporated, such as the adoption of clear and elegant statements. A few more exercises have been added with relevant hints when necessary.Reviews from the Second Edition:“The books cover a large amount of mathematics. They are 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 “The exercises at the end of each section supplement the material of the section nicely and provide a good chance to develop additional intuition and deeper comprehension. 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, zbMATH

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Product details

Series: Graduate Texts in Mathematics (Book 250)

Hardcover: 624 pages

Publisher: Springer; 3rd ed. 2014 edition (November 14, 2014)

Language: English

ISBN-10: 9781493912292

ISBN-13: 978-1493912292

ASIN: 1493912291

Product Dimensions:

6.1 x 1.4 x 9.2 inches

Shipping Weight: 2.4 pounds (View shipping rates and policies)

Average Customer Review:

5.0 out of 5 stars

5 customer reviews

Amazon Best Sellers Rank:

#1,059,622 in Books (See Top 100 in Books)

Very useful book in very good conditions

As described.

this is the volume 2 of Grafakos' books. it contains much more advanced topics than volume 1. I like the way Grafakos arranges different topics, and the exercises are especially good for study.

The book was in perfect conditions

There are a lot of good books on Fourier Analysis. If you're just starting, I think Elias Stein's Fourier Analysis textbook is a good start. There are very few texts that prove L. Carleson's theorem or (better) Hunt's extension to it. The theorem is just too hard for most contexts. But, if you don't know that basic result, I think you're missing a lot. So, this is a more complete book and should be considered valuable, although not, I think, a first textbook. Folland's book is good, too, although I don't like the fact that he quotes basic theorems without proof so that he can get on to more advanced topics. It's a trade off. Somebody had to do it. Folland did it. I don't really see how a person could avoid buying and reading this book, although the temptation is certainly there. Fourier things are deep, but they are also detailed and can be boring.

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Get Free Ebook The Jungle Grows Back: America and Our Imperiled World

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Audible Audiobook

Listening Length: 5 hours and 44 minutes

Program Type: Audiobook

Version: Unabridged

Publisher: Random House Audio

Audible.com Release Date: September 18, 2018

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So . . . which of them is more nearly right -- Kagan or Kennedy?Kagan warns that American listlessness in foreign policy risks letting what he calls "the Liberal Order" that has made the Postwar world so incredibly prosperous and peaceful -- his "garden" -- disappear into an encroaching jungle of repression and war. He (rightly, in my opinion) argues that such a brutish and nasty world is the historic norm. He also argues (again, I would say rightly) and American firepower has, until now, tended the garden and caused it to flower. Like the Pax Romana, or that period during which Britannia ruled the seas, America's enlightened self-interest more or less has kept the peace at gunpoint. Good for us and good for the world and let's have more of it!Paul Kennedy, on the other hand, warned us years ago in his "The Rise and Fall of Great Powers" that "imperial overstretch" is what did in prior great empires. A desire to police everything, everywhere inevitably weakened and demoralized the policemen. Great powers, that is, commit suicide by stretching themselves too thin and engaging too often in armed intervention.The two views cannot be reconciled. In the aftermath of the Vietnam debacle it was Kennedy who seemed like a prophet for our time. But, since the election of Mr. Trump as president, more and more pundits urge that the USA stay active (nosy?) throughout the world and so commit the world to individual rights, "whirrled peas," unfettered international trade and . . . well, you know. (Just read Paul Klugman -- if you can stand to do so.)Kagan argues like one of the long-forgotten Empire Loyalists, a tweedy group of English, chiefly led by former colonels in the British indian Army, who argued in the last century that the British Empire was a boon and blessing to humanity (who else would have put an end to suttee?) and that world peace and prosperity depended on a strong, vigorous and assertive England. Turns out they were right.England's problem was that it just no longer had the horses to do the job. The Great British Public seemed not to give a hoot about the Empire, battleships are damned expensive and the international climate of opinion (typlified by FDR) scorned imperialism. So, by 1938 the British battle-line was a creaking collection of rusty tea-kettles while Alf and Mrs. Alf wanted peace at any price. We know what followed.Kagan makes a good argument -- for the Past. But, it is not 1946, the American people are not boundlessly optimistic any longer (thanks, in large part, to academics like Kagan with their inherent anti-Americanism) and the nation is more divided against itself than at any time since the lead-up to Civil War.America has relatively reduced economic and military power --- but you would hardly know that from reading "The Jungle Grows Back." Patriotism has long since been condemned as a failing of the "Rednecks" ("America was really never that great" -- Gov. Cuomo) and Vietnam and Iraq sobered us all up about other people's fights.I remember America of the immediate Postwar. It had unrivaled economic strength (no more!) and a sense of mission. Now, some public schools will not even let classes say the Pledge of Allegiance each morning. Everything Kagan writes about the Past is true -- but it does not apply to the Future.America is a deeply divided nation in slow relative decline. Its people increasingly are divided into mutually hostile identities and cynicism is the order of the day.Kagan's tribute to the America of FDR, HST, Ike, Acheson, Dulles, Marshall . . . and all the other great figures of the 20th Century is touching and, if you are my age, it breaks one's heart. But, today's America cannot even decide the difference between a boy and a girl for itself -- it's not about to lead a new Great Crusade.Sic transit gloria.

Excellent analysis of the last seven decades of relatively peaceful cooperation among nations, and the dangers of taking the "American-made liberal world order" for granted. Kagan reminds those who clamor for more isolationism that without the continuing full involvement of the United States in every part of the globe -- yes, as the world's policeman and as the best model of democratic capitalism -- the world order can very rapidly fall apart. He analyzes the history (most recently in the first half of the 20th century) of how fragile democracies can easily devolve into authoritarian, fascist systems. He confronts the truth of hypocrisy, immorality and even egregious error in American geopolitical calculations but demonstrates quite convincingly that this is the best we have in a time of rising right-wing nationalism worldwide. Kagan insists that the United States must continue to support its allies economically and militarily and must continue to support a cohesive European Union, which is in danger of coming apart. Very persuasive, a must read.

I don't think I have ever read a book that consists entirely of generalizations and opinions before this one. Strangely, I found it compelling in spite of a contrarian desire to challenge the thesis: that without the military protection of the USA the "liberal world order" is doomed to succumb to authoritarian regimes. The author traces recent history for support of his point of view and cites an impressive bibliography. His thesis is clearly and persuasively presented. I am nearly convinced. His overall view that there is no imperative based on history or human nature for preservation of the "liberal word order" is certainly correct. History is not over and human nature has not changed since the end of WWII. His insistence on the phrase "liberal world order" is curious; most would say "the free world" or simply "the West." But I believe the author clearly makes his case, arguable though it may be, that the USA must stay involved in international affairs, even to the point of military involvement, to preserve the way of life we have enjoyed since the second world war.

Author fears that the US is backing away from being the worlds peacekeeper. He bemoans this and wants to keep the US in that role. Most other nations want that also, I believe, although they do not want to pay for it.

An essential book by R. Kagan. He explains that it is not the first time that in America, there are calls to stop engaging the world, always to unintended mostly bad consequences. He argues in the clearest arguments I’ve ever read, that it is in the best interests of the Americans themselves, to be the world’s policeman. Who else, China or Russia? Or Canada? Only the US can assume the role. Mistakes are made, and the results are not a perfectly peaceful world, but the opposite could be much worse. Relative peace created the conditions for the mighty dollar and exponential increase in trade. America stopped two world wars to great costs human and treasury: what if they had intervened earlier and stopped Hitler or Stalin in their tracks before they got too big for their own boots. Obama didn’t engage in the “stupid war” in Syria resulting in millions dead or displaced. Maybe containment is the best we could hope for in a not perfect world. As the title’s imply: when a garden is not tended, the jungle grows back.

A must read for voters, and certainly every politician. The book is small but dense with a well reasoned argument that the world would return to waring regional powers without the United States to maintain the Liberal world order it has assumed after World War II. Perhaps. His argument is frightening enough to be taken seriously.

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