Your overview videos are not only great introductions for the uninitiated, but are excellent reviews for those needing a refresher on the subject. Please keep posting overview videos. You are providing a valuable contribution to the mathematics and science communities.
Thank you!! I am studying maths, and this gave me a quick reminder of some definitions n theorems. You are a very nice person, and you make the world better.
Thanks! And let me point out, that the friendly atmosphere you have makes the topic even more appealing than it is for itself already. 19:45 bless you, by the way
The material certainly did not excite me on first encounter but your enthusiasm is so infectious. Am reviewing this material to properly understand the mathematical spine of quantum mechanics and you’ve inspired me to take it back up with a different attitude. Thanks professor!
Thank you for the video Engineering student here (2nd year) and considering taking a functional analysis module available in a Master's program that I'm interested in. This video was very helpful since I wanted to know the main topics of functional analysis
Dr. Peyam, I am one of your subscribers, who has fallen in love with math after watching your approach to mathematics. I am currently studying functional analysis for my masters and I would love it if you kindly consider to suggest some comprehensive books in functional analysis that contain topological and measure theoretic preleminaries, normed spaces, topological vector spaces, banch algebra, operator theory, hilbert & sobolev spaces, distribution theory, harmonic analysis, integral equations, functional equations, c*-algebras etc in one volume. Thank you for this overview, it is valuable for my learning.
@@drpeyam I don't know Marc Rieffel, but I knew his PhD supervisor, Richard Kadison, as I spent a year visiting University of Pennsylvania whilst a PhD student (I was based at Manchester University). Alas Kadison died in August. Kadison and Ringrose wrote the well known Fundamentals of the theory of operator algebras. And Ringrose was my supervisor's supervisor, working at Newcastle University, where I did my post doc.
Had my first lecture in functional analysis today, and it wasn't really clear to me what functional analysis was about. Thanks to this video I now kind of know what I'm doing, and I understand the proofs! Thanks Dr. Peyam!
I have a question though... We saw that the differentiation linear transformation is not continuous, but if we have f,g real functions, it is true that: (a*f + b*g)’ = a*f’ + b*g’ , for a,b constant. Doesn’t it imply continuity of the differentiation linear transformation?
Only just done calculus 3 but watched every minute. Also I think calling functional analysis a sub-field is an understatement. Hilbert spaces are in just about everything!
Great introduction! Full of intuition and motivating examples -- I think these are the stuff that many non-mathematicians can remember in the long run. Would it be possible to do a series of videos on functional analysis?
do you by any chance also follow generative models in machine learning? it would have a huge audience if you grounded the abstract proofs in say Wasserstein GAN or improved training articles.
Hi Dr Peyam @Dr Peyam, can u solve this convex function problem [written in latex] ? PLZ 🙏 One is seeking an example of a function $f:\mathbb{R}^2 ightarrow \mathbb{R}$ so that: \\ $f \in C^k k\geq 2, \frac{\partial f}{\partial x_1} eq \frac{\partial f}{\partial x_2}$ \\ $f$ is globally quasi-convex and at no point convex.\\ In addition, there exists another function $g:\mathbb{R} ightarrow \mathbb{R}$, $g\in C^k, k\geq 2$, monotonically increasing, so that $g \circ f$ is globally strictly convex. If possible, find such $f$ and $g$. If impossible, explain why.
Hi Mr i have a question off topic please I'm searching for an explicit formula of this spaces $$C^{4+\alpha}(\overline{\Omega})$$ plz any one have an answer help me
Your space is the set of functions that are 4 times differentiable, and whose 4th derivative is Holder continuous of order alpha, that is |f””(x) - f””(y)|
Thank you so much Sir . Please suggest some good books of functional analysis . I'm beginner & I'm really motivated by your Lectures. It looks easy now . I never try to understand before but your way of teaching is outstanding.
In the proof that bounded and continuous are equivalent, I thought that delta might depend on x? Don't you need to know that T is uniformly continuous to conclude that delta is independent of x?
@@drpeyam Ah so continuous linear functionals are always uniformly continuous? That's so cool! Thanks for the reply, I had no idea. Functional analysis truly is heaven for analysts.
@23:50 You said if V = V** then V is reflexive ! This is wrong , you are missing something ! Actually the isomorphism that makes this equality , it really matters.
Your overview videos are not only great introductions for the uninitiated, but are excellent reviews for those needing a refresher on the subject. Please keep posting overview videos. You are providing a valuable contribution to the mathematics and science communities.
Thanks so much!!!! 😄
Incredible! The most efficient one hour I spent on TH-cam. Thanks so much, Dr. Peyam. You're awesome.
Thank you!! I am studying maths, and this gave me a quick reminder of some definitions n theorems. You are a very nice person, and you make the world better.
So nice, as always!
50 min of functional analysis is just what I needed =)
"Alright, thanks for watching!"
No, thank you!
Thanks! And let me point out, that the friendly atmosphere you have makes the topic even more appealing than it is for itself already.
19:45 bless you, by the way
I was having a rough day. Came home to 50 mins of Dr. Peyam reviewing functional analysis. A very satisfying end to an otherwise rough day. Thanks.
Awwww, glad I could make your day!!!
The material certainly did not excite me on first encounter but your enthusiasm is so infectious. Am reviewing this material to properly understand the mathematical spine of quantum mechanics and you’ve inspired me to take it back up with a different attitude. Thanks professor!
Thanks so much!!!! 😊😊
This is the single greatest video I've seen in the past 3 years.
Great 3000ft overview! It's so easy to get lost in the trees of functional analysis (e.g. which results hold for p=1 or infinity). Super helpful!
This video is great for researchers in other fields who have encountered functional analysis "in the wild" but never studied it yet. Thanks!
Thank you for the video
Engineering student here (2nd year) and considering taking a functional analysis module available in a Master's program that I'm interested in. This video was very helpful since I wanted to know the main topics of functional analysis
Anyone else whatched this until the end like me? Damn! cool video Dr peyam!
heard a good joke in my last lecture
what is a yellow, complete and normed vektorspace? a Bananach space
Dr. Peyam, I am one of your subscribers, who has fallen in love with math after watching your approach to mathematics. I am currently studying functional analysis for my masters and I would love it if you kindly consider to suggest some comprehensive books in functional analysis that contain topological and measure theoretic preleminaries, normed spaces, topological vector spaces, banch algebra, operator theory, hilbert & sobolev spaces, distribution theory, harmonic analysis, integral equations, functional equations, c*-algebras etc in one volume. Thank you for this overview, it is valuable for my learning.
I love functional analysis by Brezis
@Dr Peyam thank you Sir very much.
Yay I’ve always been curious about functional analysis
Thanks, Dr. Peyam, I really appreciated this. It took me way back to when I did my PhD in operator algebras, specifically C*-Algebras.
OMG, do you know Marc Rieffel? I took functional Analysis with him at Cal, as well as C* algebras
@@drpeyam I don't know Marc Rieffel, but I knew his PhD supervisor, Richard Kadison, as I spent a year visiting University of Pennsylvania whilst a PhD student (I was based at Manchester University). Alas Kadison died in August. Kadison and Ringrose wrote the well known Fundamentals of the theory of operator algebras. And Ringrose was my supervisor's supervisor, working at Newcastle University, where I did my post doc.
Yeah, I’ve heard, may he Rest In Peace 😢
Had my first lecture in functional analysis today, and it wasn't really clear to me what functional analysis was about. Thanks to this video I now kind of know what I'm doing, and I understand the proofs! Thanks Dr. Peyam!
I have a question though...
We saw that the differentiation linear transformation is not continuous, but if we have f,g real functions, it is true that:
(a*f + b*g)’ = a*f’ + b*g’ , for a,b constant. Doesn’t it imply continuity of the differentiation linear transformation?
No, linearity doesn’t imply continuity in infinite dimensions
Only just done calculus 3 but watched every minute. Also I think calling functional analysis a sub-field is an understatement. Hilbert spaces are in just about everything!
I love your enthusiasm. :D
I concur with everyone else, this is really good stuff!
You are my saviour.
Great introduction! Full of intuition and motivating examples -- I think these are the stuff that many non-mathematicians can remember in the long run. Would it be possible to do a series of videos on functional analysis?
Perhaps I may interest you in my PDE playlists?
@@drpeyam let me check them out! Thanks!
do you by any chance also follow generative models in machine learning? it would have a huge audience if you grounded the abstract proofs in say Wasserstein GAN or improved training articles.
Hi Dr Peyam @Dr Peyam, can u solve this convex function problem [written in latex] ? PLZ 🙏
One is seeking an example of a function $f:\mathbb{R}^2
ightarrow \mathbb{R}$ so that: \\
$f \in C^k k\geq 2, \frac{\partial f}{\partial x_1}
eq \frac{\partial f}{\partial x_2}$ \\
$f$ is globally quasi-convex and at no point convex.\\
In addition, there exists another function $g:\mathbb{R}
ightarrow \mathbb{R}$, $g\in C^k, k\geq 2$,
monotonically increasing, so that $g \circ f$ is globally strictly convex.
If possible, find such $f$ and $g$. If impossible, explain why.
Do you have a full course online for functional analysis?
Not really but check out the book by Brezis, it’s very good
Any book recommendation for functional analysis?
Yes! My favorite one is the functional Analysis book by Brezis (freely available, I think), but also Lax is great, and so is Stein and Shakarchi
thank you, sir. Could you do one for harmonic analysis, please?
Hi Mr i have a question off topic please I'm searching for an explicit
formula of this spaces
$$C^{4+\alpha}(\overline{\Omega})$$
plz any one have an answer help me
Your space is the set of functions that are 4 times differentiable, and whose 4th derivative is Holder continuous of order alpha, that is |f””(x) - f””(y)|
amazing introduction , you squeeze 3 months in 49 min 🙏
44:50 Hilbert Space; it has dot product.
wow this is awesome🔥
Thank you so much Sir . Please suggest some good books of functional analysis . I'm beginner & I'm really motivated by your Lectures. It looks easy now . I never try to understand before but your way of teaching is outstanding.
I like the book by Brézis a lot
Now I watch Peyam in 60 fps. So dynamic... woooh!
Thanks for the overview. :)
what a wonderful video, thanks a lot
After this video, I challange you to make a mathematically rigorous series on quantum mechanics.
This is magical !
This is pure gold
In the proof that bounded and continuous are equivalent, I thought that delta might depend on x? Don't you need to know that T is uniformly continuous to conclude that delta is independent of x?
That’s the beauty of it, in functional continuity is the same as uniform continuity
@@drpeyam Ah so continuous linear functionals are always uniformly continuous? That's so cool! Thanks for the reply, I had no idea. Functional analysis truly is heaven for analysts.
This is very good.
Please make a lecture about soboleve space
Sir, please suggests a best functional analysis book
Brezis
What level of my degree would I study this? It's very interesting buy I have only just started analysis and group theory. :(
Beginning of grad school
@@drpeyam Okay nice!
Hey Peyam :)
Are you planning to make a video about Ito Formula and stochastic differential euqations?
Great idea! Also great username 🙂
Great! thank you :)
Viele liebe Grüße aus Deutschland !
16:55 no sup for you! He is not only good at teaching mathematics. Making people jaw dropping is his second nature.
Thank you for the video!
冒頭3分しか見てないけど、え、ノルムドベクタースペース+コンプリート=バナッハスペースなのん それだけだったの？？？
peyam you got a favorite book on this subject?
Yep, the book by Brezis. Lax is good too, and so is Stein & Shakarchi
At the end, you kept saying "in the separable case," but most Hilbert spaces aren't separable, so these results are very limited
24:48 See? This is the best dropping..
I wish I had time to only watch these Peyams
@23:50 You said if V = V** then V is reflexive ! This is wrong , you are missing something ! Actually the isomorphism that makes this equality , it really matters.
Interesting, you’re right! Learned something new today :)
Awesome
This is gold
19:45 24:50 27:13 35:35
MrTanorus Hahahahahahaha
Nice
Thankssssssss
The correct velocity is 1.25 :D
Hahaha
Thank You very much! No soup for you😂😂
Gem
I'm hanging out for your 31.4159265359...th Birthday Special show.
Should be a doozie!!
Thank You, but I was looking for a video on functional analysis in systems engineering.
I'm hanging out for your 31.4159265359...th Birthday Special show.
It should be a doozie!!
nth
HECK YES MY DUDE
I'm Third. :-)
1st