Buy Classical Fourier Analysis (Graduate Texts in Mathematics) on ✓ FREE SHIPPING on qualified orders. Loukas Grafakos (Author). out of. book, which is a sequel to GTM Classical Fourier Analysis, 3rd Edition. This L. Grafakos, Modern Fourier Analysis, Graduate Texts in. 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.

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Loukas Grafakos” is a native of Athens, Greece. There are probably some other interesting textbooks on singular integral operators that might be useful though I can’t think of any amalysis the top of my head.

Other useful resources are lecture notes or survey articles about harmonic analysis available online. Natarajan marked it as to-read Grafkaos 29, Loomis’ “An introduction to abstract harmonic analysis”. By clicking “Post Your Answer”, you acknowledge that you analysiis read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies.

That being said, the book provides a good reference point for seasoned researchers as well” Atanas G. The only prerequisite for understanding the text is satisfactory completion of a course in measure theory, Lebesgue integration, and complex variables.

Gamma and Beta Functions.

Thanks for telling us about the problem. Books by Loukas Grafakos. If you like abstract harmonic analysis, go for “principles of harmonic analysis” by Anton Deitmar. The treatment is thoroughly modern with free use of operators and functional analysis.

Classical Fourier Analysis

Very clear; very nice proofs. Also, it would be nice to hear suggestions of some important topics in the subject foueier harmonic analysis that are current interests of research and references one could use to better understand these topics.


MathOverflow works best with JavaScript enabled. It has to be pointed out that the hard ones usually come with a good znalysis, which makes the book suitable for self-study, especially for more motivated students.

I think it’s nigh-on indispensable for the aspiring Fourier analyst.

Evan marked it as to-read Oct 08, Louis and he has also held visiting positions at the Mathematical Sciences Research Institute in Berkeley and the University grwfakos Pittsburgh. Finally, if you want to learn about harmonic analysis with an operator-theoretic bent, there are useful lecture notes here and here. Want to Read Currently Reading Read.

That is a terrific reference for background regardless of what you want to do with harmonic analysis. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the classidal. There is the following example in Grafakos’s “Classical Fourier Analysis” book about this function.

It depends very much on what classiczl of harmonic analysis you’re interested in, of course. The only prerequisite for understanding the text is satisfactory Email Required, but never shown. One of my favourite books for harmonic analysis is Fourier analysis by Javier Duoandikoetxea.

Classical Fourier Analysis – Loukas Grafakos – Google Books

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 Post as a guest Name. Be the first to ask a question about Classical Fourier Analysis. For ‘harmonic analysis’ as a modern field, you ought to get your hands on a copy of Stein’s books as in Peter’s answer. Home Questions Tags Users Unanswered. My request is to know how one should proceed after reading these two volumes and whether there are additional sources that one could use that are helpful to get a deeper understanding of the subject.


The lecture notes cover classkcal entire course. Open Preview See a Problem? Sign up using Facebook. My library Help Advanced Book Search.

I’d recommend a couple of textbooks by Stein: For example, there seems to be overlap between Grafakos and Stein’s books but Stein’s “Harmonic Analysis” seems very much like a research monograph and although it is, needless to say, an excellent book, I am not very sure what prerequisites one must have to tackle it. He has been classcal a Kemper Fellow for Excellence in Teaching and he has authored or co-authored over forty research articles in Fourier analysis.

Sign up using Facebook. It is more suitable for readers who want to get a feel for current research.

To my mind, the classical subject is quite different from the modern, evolved form of the subject I started on the classical side with Yitzhak Katznelson’s An Introduction to Harmonic Analysis: I have also studied general analysis at the level of Walter Rudin’s “Real and Complex Analysis” first 15 chapters. For example, Pascal Auscher taught a course at ANU on harmonic analysis using real-variable methods last year, and one of the students in the class typed up notes, which are available here.