So glad that you're making a serie about Spectral Theory, I'm not quite there yet in my studies but I was always fascinated by the topic. Your videos really inspire me to study math even more.
I am electrical engineer. Took course in spectral analysis. What you taught is similar to the basics of our course. The beauty is the concepts you taught can be used to compute pseudoinverse for non square matrices. This has applicatioms in detection amd estimatiom
Hello vetri. Naan functional analysis ku neraya application irukunu kelvi patruken but electrical engineering la application irukum nu theriyathu. So can you enlighten me a little. I mean neenga spectral theory padika thevai enna or just pure interest. Just curious.
Great man, keep going please complete the spectral and other important theorems fast, also your search result is almost top in India so don't worry you will get lots of views once syllebus is completed, I did not much of measure they your lectures were blessing 😊😊
Excellent. But I have a question. If the spectrum consists of both countable and Continuum eigenvalues then what is the dimension of the Banach space is it countable or uncountable? Actually I'm from physics background and we use position and momentum basis where the spectrum is Continuum. But there are other operators (self adjoint) for the same system whose spectrum is countable and their eigenvalues forms a complete set. So what is the dimension of the space?. Also I have another request can you do separate video on topological vector spaces. The book I'm reading starts with it but I don't see using that later in the book. So can you explain how topological vector space plays a role in functional analysis? Thank you.
Very good questions! Let me tackle them in future videos because there is not short answer. Especially when you are looking at operators from quantum mechanics that are usually unbounded.
Many main theorems are also proved after the introduction of topological vector spaces. Some beginning functional analysis texts takes such route. I don't know why or the differences between learning the subject not having seen the concept versus books which introduces it early. I mean, why is the concept important and does it allow one to prove classical theorems more easily or do they cover different mathematical circumstances.
You need topological vector spaces in a lot of applications. For example, if you want to explain distributions, it is very helpful. However, I think that starting with them, is overkill for the beginning. Metric spaces are abstract enough when you start with functional analysis :D
I really wanted to watch your videos, but your channel doesn't have subtitles turned on to allow the inclusion of more people ): I hope you read this and that when I come back I can be part of your subscribers.
By the way: it is simply not true that my channel has "subtitles turned off". A lot of my videos have subtitles contributed by nice viewers. My measure theory series even has Spanish subtitles, which allow the inclusion of more people.
@@brightsideofmaths OK. But this video, for example, has no subtitles. What I claim and suggest is that TH-cam auto-generated subtitles are turned on because users can no longer add subtitles.
@@_Cristina Auto-generated subtitles are activated but this is not a safe bet. Sometimes they are generated, sometimes not. This is not my choice. Therefore, in the case, you want subtitles for a particular video (e.g. this one), you could simply ask me.
@@brightsideofmaths I am happy with your helpfulness and I am now a subscriber to your channel. And yes, I'd love for this video to have subtitles, in fact, for every video to have, so that I don't have to ask directly. I'm really, really interested in your content, but my English isn't good enough to understand everything that is said, so I do need automatic subtitles, not just the manual subtitles.
![Functional Analysis 28 | Spectrum of Bounded Operators [dark version]](http://i.ytimg.com/vi/kBbDtq7Aki4/mqdefault.jpg)
So glad that you're making a serie about Spectral Theory, I'm not quite there yet in my studies but I was always fascinated by the topic. Your videos really inspire me to study math even more.
This is an excellent introduction. The video is a moderately advanced introduction, although spectral theory is an advanced topic. Excellent work.
I am electrical engineer. Took course in spectral analysis. What you taught is similar to the basics of our course. The beauty is the concepts you taught can be used to compute pseudoinverse for non square matrices. This has applicatioms in detection amd estimatiom
Hello vetri. Naan functional analysis ku neraya application irukunu kelvi patruken but electrical engineering la application irukum nu theriyathu. So can you enlighten me a little. I mean neenga spectral theory padika thevai enna or just pure interest. Just curious.
@@weirdo-jw9kc Spectral theory naraya applocation irukku. Radar la namma signal anupnomna periya antenna andha signal vangikkum. Antenna ngradhu othai antennava irukaadhu. Adhu neraya chinna antenna va vechurukkum. Namma anupra signala correct a estimate pannanum. Apdi pannati, gora goranu satham kekum (white noise). Andha noise ah koraikrakaaga namma spectral analysis yse pandrom
Thank you for the lecture !!!!! I have been struggle with the math behind Quantum Mechanics for a long time. The topics is very well explained
Please continue your teaching towards Pure mathematics..... 🎉❤
Yeah, I will do it :)
Great man, keep going please complete the spectral and other important theorems fast, also your search result is almost top in India so don't worry you will get lots of views once syllebus is completed, I did not much of measure they your lectures were blessing 😊😊
Great explanation, as always!
Excellent. High quality.
Thank you for doing these videos!
I have to say the same as Dywww. Thanks for your presentation. Where did you do your presentation normally (on which University)? Best regards. Dieter
My request has been answered. Thanks!
Spectral theory is a very wide topic. I need some more videos to cover it nicely :)
Thank you for these videos
I look forward to seeing next lecture!!
You are doing a wondaful work keep on
Many many thanks
Thank you sir..
Waiting for the next video with some fascinating examples and your always inspiring explanation...😇😇😇
Next video is coming this week :)
Excellent. But I have a question. If the spectrum consists of both countable and Continuum eigenvalues then what is the dimension of the Banach space is it countable or uncountable? Actually I'm from physics background and we use position and momentum basis where the spectrum is Continuum. But there are other operators (self adjoint) for the same system whose spectrum is countable and their eigenvalues forms a complete set. So what is the dimension of the space?. Also I have another request can you do separate video on topological vector spaces. The book I'm reading starts with it but I don't see using that later in the book. So can you explain how topological vector space plays a role in functional analysis? Thank you.
Very good questions! Let me tackle them in future videos because there is not short answer. Especially when you are looking at operators from quantum mechanics that are usually unbounded.
@@brightsideofmaths thank you. Excited for future videos!
Nice explanation..
Thanks!
Thank you
Any more videos coming?
Yes, of course!
Can you also do some lecture videos on topological vector spaces within functional analysis please. :)
Many main theorems are also proved after the introduction of topological vector spaces. Some beginning functional analysis texts takes such route. I don't know why or the differences between learning the subject not having seen the concept versus books which introduces it early. I mean, why is the concept important and does it allow one to prove classical theorems more easily or do they cover different mathematical circumstances.
You need topological vector spaces in a lot of applications. For example, if you want to explain distributions, it is very helpful. However, I think that starting with them, is overkill for the beginning. Metric spaces are abstract enough when you start with functional analysis :D
thx
I really wanted to watch your videos, but your channel doesn't have subtitles turned on to allow the inclusion of more people ):
I hope you read this and that when I come back I can be part of your subscribers.
I have read it and you can be part of my subscribers now :)
By the way: it is simply not true that my channel has "subtitles turned off". A lot of my videos have subtitles contributed by nice viewers. My measure theory series even has Spanish subtitles, which allow the inclusion of more people.
@@brightsideofmaths OK. But this video, for example, has no subtitles. What I claim and suggest is that TH-cam auto-generated subtitles are turned on because users can no longer add subtitles.
@@_Cristina Auto-generated subtitles are activated but this is not a safe bet. Sometimes they are generated, sometimes not. This is not my choice.
Therefore, in the case, you want subtitles for a particular video (e.g. this one), you could simply ask me.
@@brightsideofmaths I am happy with your helpfulness and I am now a subscriber to your channel. And yes, I'd love for this video to have subtitles, in fact, for every video to have, so that I don't have to ask directly. I'm really, really interested in your content, but my English isn't good enough to understand everything that is said, so I do need automatic subtitles, not just the manual subtitles.
Came expecting the spectrum operator from valorant… stayed for an educational video
Beautiful. I love you