Timeline for Stein's book on harmonic analysis
Current License: CC BY-SA 4.0
11 events
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| Feb 23, 2022 at 15:59 | comment | added | Onur Oktay | I'd also suggest to keep the book books.google.ca/books?id=maYDBgAAQBAJ ready on your shelf as a supplementary source. Needless to say, you should consult with your advisor with every suggestion, since harmonic analysis on $\mathbb{R}^n$ is a vast ocean, and one can easily get lost if s/he wants to conquer every corner of it at once, without the guidance of the Polaris. | |
| Feb 23, 2022 at 15:52 | comment | added | Onur Oktay | The multipliers you refer to are Fourier multipliers. You might want to check the sections in Gröchenig's book about Gabor multipliers, once you finish the (relative prerequisites) basic $L^p$ theory of Fourier series, Fourier transform, and Littlewood-Paley theory of Fourier multipliers. | |
| Feb 23, 2022 at 15:47 | comment | added | Onur Oktay | Stein's book covers Pseudodifferential operators (PDOs) extensively from a classical viewpoint. I'd suggest to look into the short-time Fourier transform and its relation with PDOs. You can skim through Gröchenig's book books.google.ca/books?id=yTnTBwAAQBAJ to have a feeling about the subject at this stage. | |
| Feb 23, 2022 at 15:47 | comment | added | Onur Oktay | 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. | |
| Feb 23, 2022 at 9:06 | comment | added | Z. M | 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). | |
| Feb 23, 2022 at 9:04 | history | edited | YCor | CC BY-SA 4.0 |
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| Feb 23, 2022 at 8:25 | comment | added | Jean Marie Becker | "The image processing handbook" John C. Russ | |
| Feb 23, 2022 at 8:02 | comment | added | Ben McKay | @JeanMarieBecker: could you recommend some great books or articles for the harmonic analysis student on the applied side? | |
| Feb 23, 2022 at 7:59 | comment | added | Jean Marie Becker | 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. | |
| S Feb 23, 2022 at 7:03 | review | First questions | |||
| Feb 23, 2022 at 9:35 | |||||
| S Feb 23, 2022 at 7:03 | history | asked | risefrominfinite | CC BY-SA 4.0 |