I'm watching this before my finals, no apparent reason. I just forget all the math I know before exams and get hypertension. I'll update yall if I pass
@@hewhoyawns315 Nope, just never got sent the zoom link. Sent an email but it was Friday so I've most likely got to wait until Monday to hear back. Oh well.
Hi buddy. Your videos inspire me to study mathematics. Actually I was admitted in MSc in mathematics and computing. My college just ruined our semesters by forcing options that we didn't want to study. After college I worked as a software engineer but I never enjoyed software engineering the way I used to enjoy mathematics. It's been 5 years since I opened a mathematics book and I feel like I forgot more than 50% of what I knew 😂. Your videos are reigniting my interest in mathematics and I don't know why but Fourier analysis is like catching my attention. Keep making these videos and keep inspiring
Looking at the amount of books you have, I am curious, how was your first experience with functional analysis / operator theory? Did you struggle with it at all, or was it at a point where you were more "principled" with studying? Because imo, it's changed quite a few of my learning habits and understanding. It's incredibly powerful!
Another proof for the (*) you had missing could be as follows: f(x) is analytic on the real line and non constant so at every point in the interval there exist some open neighborhood where f is analytic with radius R_i by definition of analyticity. Choose the minimum of these R_i (call it R_min) which have to be countable as that compact segment of the real axis has a finite subcover. Then you have an open rectangle with height R_min and f is certainly analytic on T X [R_min*i/2, - R_min*i/2], define F to be the analytic continuation of f(x) on the lines x + R_min*i/2, x - R_min*i/2 and since F is analytic and on a line (analytic on a line and on some open set around the line means non constant), its non constant and by the permanence principle of analytic continuation you're intersecting on a non-discrete set so F is the unique direct analytic continuation of f. qed. Hope this helps/brings a different idea to the table, really like the content and its really fun seeing some harmonic analysis and the coefficients relating to f being C infinity!
He doesn't use a textbook but I have some recommendations that helped me: 1. Introduction to Harmonic Analysis - Katznelson 2. Fourier Analysis - Stein and Shakarchi 3. Classical and Modern Fourier Analysis - Grafakos
@@PhDVlog777 isn't fourier analysis easier if you already have a course in functional analysis covering distributions, convolution and operation calculus. I mean you have to heard about the famous fouruer transform and the super famous poisson summation formula which is like Euler Maclaurin summation on steroids. But poisson summation over number fields is feeding in steroids, methamphetamine and crack cocaine all at once.
Sam Sulek of mathematics
Hahahhahahahahahahahaha
I'm watching this before my finals, no apparent reason. I just forget all the math I know before exams and get hypertension. I'll update yall if I pass
wishing you the best!
Good luck, you got this!!
Watching this to calm myself down before a PhD interview
Update: I got in!!!
Good luck!!
you got this!
Interviewer never showed up 🙃
@@blakewilliams1478 What ... What happened? Did anyone call you or anything? Sorry that happened to you bud, that's rough...
@@hewhoyawns315 Nope, just never got sent the zoom link. Sent an email but it was Friday so I've most likely got to wait until Monday to hear back. Oh well.
Hi buddy. Your videos inspire me to study mathematics.
Actually I was admitted in MSc in mathematics and computing. My college just ruined our semesters by forcing options that we didn't want to study. After college I worked as a software engineer but I never enjoyed software engineering the way I used to enjoy mathematics.
It's been 5 years since I opened a mathematics book and I feel like I forgot more than 50% of what I knew 😂.
Your videos are reigniting my interest in mathematics and I don't know why but Fourier analysis is like catching my attention.
Keep making these videos and keep inspiring
I noticed The Book of Proof on your table. I’m studying from it right now! It presents information in a really nice way I think
I'm taking a course in measure theory this semester, really looking forward to your vids!
What lighting are you using? Looks really good!
Pls share your recipe for the lim soup
Thanks for the video! What pen are you using?
Make a video about Euler and Gauss, please
Looking at the amount of books you have, I am curious,
how was your first experience with functional analysis / operator theory?
Did you struggle with it at all, or was it at a point where you were more "principled" with studying?
Because imo, it's changed quite a few of my learning habits and understanding. It's incredibly powerful!
Hi babe
heyyyy
Another proof for the (*) you had missing could be as follows: f(x) is analytic on the real line and non constant so at every point in the interval there exist some open neighborhood where f is analytic with radius R_i by definition of analyticity. Choose the minimum of these R_i (call it R_min) which have to be countable as that compact segment of the real axis has a finite subcover. Then you have an open rectangle with height R_min and f is certainly analytic on T X [R_min*i/2, - R_min*i/2], define F to be the analytic continuation of f(x) on the lines x + R_min*i/2, x - R_min*i/2 and since F is analytic and on a line (analytic on a line and on some open set around the line means non constant), its non constant and by the permanence principle of analytic continuation you're intersecting on a non-discrete set so F is the unique direct analytic continuation of f. qed.
Hope this helps/brings a different idea to the table, really like the content and its really fun seeing some harmonic analysis and the coefficients relating to f being C infinity!
What do you record with?
Vincent which building did you room in freshman year
You gonna do research in Fourier/harmonic analysis?
The « idea » at the end looks really good. Don’t we also need some form of connectedness for the identity theorem?
what textbook did both of your fourier courses used can i ask?
He doesn't use a textbook but I have some recommendations that helped me:
1. Introduction to Harmonic Analysis - Katznelson
2. Fourier Analysis - Stein and Shakarchi
3. Classical and Modern Fourier Analysis - Grafakos
I did a grad level Fourier analysis class last semester, we used Duoandikoetxea or something, pretty decent imo
@@PhDVlog777 isn't fourier analysis easier if you already have a course in functional analysis covering distributions, convolution and operation calculus. I mean you have to heard about the famous fouruer transform and the super famous poisson summation formula which is like Euler Maclaurin summation on steroids. But poisson summation over number fields is feeding in steroids, methamphetamine and crack cocaine all at once.