Amazing content and I still can't believe I find such high quality overview for free. Thank you for all the effort you put into making these videos!

Amazing overview! Thank you for all your effort in putting Koopman's theory in a nice, easily-digestible fashion! Keep you your amazing work!

Thanks for including references, I read these after your presentation. Well done. Thanks

This is a great presentation. I learned a lot from the presentation. Thanks!

Very good explained , thank you for this brilliant introduction.

I have several published papers on the so-called Koopman-von Neumann Hilbert space representation of Hamiltonian mechanics, yet I know very little about the Koopman operator theory. I feel like there is a language barrier that makes it hard for me to study this topic, so I'm glad that these videos exist.

I wish I could have seen this earlier. Thank you!

Thanks for this amazing introductory series on the Koopman operator! Really enjoy the conceptual emphasis on this framework (reminds me of feedback linearizations). I was wondering whether you meant X to be g(X) at time 23:20, since you labeled them measurements.

Thank you so much for all your videos, your book and videos have been the basis of my data-driven dynamics/ machine learning themed bachelor's dissertation. How did people survive before youtube?

Thanks, Steve! I am doing research over resolvent mode decomposition, the paper of Ati Sharma was helpful.

Absolutely love your content Steve! Is there a relationship between the Koopman operator and Noether's theorem(s) or the Euler-Lagrange equations, or facts about either you can exploit to control or learn dynamical systems?

Thank you for the great talk! Minor issue: I believe there's a typo at @15:47 : phi_lambda should be x_2, and phi_2mu should be x_2 + (lambda - 2mu)/lambda * x_1^2

I really like these amazing videos, but I have a question. Here we are interested in a Koopman invariant subspace; however, the existence of such invariant subspace might not be even possible in general Hilbert space (as the invariant subspace problem is still an open question unless some restriction is applied). What would you think about this?

One more question. The Koopman operator is the adjoint of the Frobenius Perron operator, the latter advancing a density and the former advancing a scalar (an observable.) Is it possible to repeat all the Koopmanism stiuff with the F-P operator? Also, in the conventional use of adjoint methods, you can either advance the F_P forward in time or the K backward, taking the inner product of the scalar and the density at the initial or the final time. Does any of this appear in Koopman spectral methods or not?

Amazing!.Thank you for the lecture.Hope we will meet some day 😄

"So it's kinda nasty..." I've never thought of math can be so lively :)

At about 23:11, you mention a pseudoinverse that you get by regression. Is an inverse covariance matrix used, and if so, does it follow from the data? Excellent intro and I look forward to the other lectures.

Would you be able to post or show how the eigenfunctional was found using the laurent series?

Is there a relation with spectral theory and operator algebras and Koopman operator theory?

At about 20:52 you derive \phi(x)=e^{-1/x}. You can just as easily show that e^{-\lambda / x} has eigenvalue \lambda. So there's a continuous spectrum, and 0

is x=-1/t a solution to that differential equation @17:29 ?

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you know, after i break the delfie hellman I'm gonna enroll in your class.