Don't think I'll ever get used to stars in LaTeX when someone means simple multiplication.<p>The preceding blog post[1] seems to contain the more interesting parts though. This is just (d/dt)^n e^At x = A^n e^At x, which is kind of obvious from the definition of e^At.<p>[1]: <a href="https://nosferalatu.com/DerivativesLogarithmsTransforms.html" rel="nofollow">https://nosferalatu.com/DerivativesLogarithmsTransforms.html</a>
The previous post in the series[1], helpfully linked to in the introduction, has a lot more details of the underlying concepts.<p>It also set my mind wandering to the not-technically-related functional derivatives[2], where you vary the function slightly rather than the argument value.<p>I'm not great at math, but I do love this what-if exploration you can do in math. Due to the various proofs underlying it all it seems sometimes more fruitful than similar exploration in programming, where one might quickly stumble upon obscure compiler errors or similar obstacles.<p>[1]: <a href="https://nosferalatu.com/DerivativesLogarithmsTransforms.html" rel="nofollow">https://nosferalatu.com/DerivativesLogarithmsTransforms.html</a><p>[2]: <a href="https://en.wikipedia.org/wiki/Functional_derivative" rel="nofollow">https://en.wikipedia.org/wiki/Functional_derivative</a>
Terence Tao has a book “Higher order Fourier analysis”, can anyone chip in on whether the two are related?<p>Here is a video, it seems to focus on aaplications in number theory, but I cant tell as a layman
<a href="https://www.youtube.com/watch?v=nr2Xv9v9CZc" rel="nofollow">https://www.youtube.com/watch?v=nr2Xv9v9CZc</a><p>For example, this is the tradFourier version of what hes trying to do<p><a href="https://en.wikipedia.org/wiki/Hardy–Ramanujan–Littlewood_circle_method" rel="nofollow">https://en.wikipedia.org/wiki/Hardy–Ramanujan–Littlewood_cir...</a>
I like this summary of Lie theory in the context of robotics: <a href="https://arxiv.org/pdf/1812.01537.pdf" rel="nofollow">https://arxiv.org/pdf/1812.01537.pdf</a>