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My background :

I am a Math PhD student. I will most probably work in harmonic analysis on Euclidean spaces. I am a fan of Folland's Real analysis and I have thoroughly studied first 8 chapters of Folland. I have a decent background in functional analysis and complex analysis. Currently, I have started learning the classical Fourier analysis by Grafakos and Stein's Singular integral book. My advisor has suggested me to finish the book Harmonic analysis : real variable methods, orthogonality, and oscillatory integrals by Stein in more or less one year.

My questions :

(i) Can one realistically finish that Stein's book in one year ?

(ii) What should be the absolutely necessary background for a person going to work in harmonic analysis on Euclidean spaces ?

(iii) My advisor has mentioned that we will most probably work in the multiplier problem. I have searched this keywords on internet but unable to find some good source or book about this topic. What are some good references to learn this multiplier problem in harmonic analysis ?

Thanks in advance.

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    $\begingroup$ You should have to look at applied harmonic analysis, the needs and deeds of thousand of people (engineers but also mathematicians) who use in particular Fourier Transform (continuous, discrete...) applied to so many diverse fields (for example the vast domain of Signal Processing). This will give you a complementary view, a large enrichment, intuition of all sort. $\endgroup$
    – Jean Marie Becker
    Commented Feb 23, 2022 at 7:59
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    $\begingroup$ @JeanMarieBecker: could you recommend some great books or articles for the harmonic analysis student on the applied side? $\endgroup$
    – Ben McKay
    Commented Feb 23, 2022 at 8:02
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    $\begingroup$ "The image processing handbook" John C. Russ $\endgroup$
    – Jean Marie Becker
    Commented Feb 23, 2022 at 8:25
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    $\begingroup$ This sort of questions is rather personal, better discussed in person, and as a student, you might consult your advisor as frequently as possible (different people have different opinions, and it depends on what your adviser expect you to know within a year, say, in order to do the research). $\endgroup$
    – Z. M
    Commented Feb 23, 2022 at 9:06
  • $\begingroup$ I understand that you're at the stage to lay a groundwork for Fourier analysis. Grafakos' two volumes are excellent resources. Duoandikoetxea's book can be a useful supplementary source. I'd suggest to stick with these books until you feel confident with your background before looking into other books. $\endgroup$
    – Onur Oktay
    Commented Feb 23, 2022 at 15:47

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