Alan C
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 Jul 5 comment If $f(x)\ll1$ is it safe to assume that $f^{\prime}(x)\ll1$? What do you mean by $f(x) \ll 1$? Perhaps relevant is the function $f_\epsilon(x) = \epsilon \sin \frac{x}{\epsilon^2}$ as $\epsilon \to 0$. Dec 1 comment Why is the area of the circle $πr^2$? Actually, Archimedes used a method of exhaustion: en.wikipedia.org/wiki/Area_of_a_disk#Archimedes.27s_proof May 21 comment showing exact functors preserve exact sequences (abelian categories, additive functors, and kernels) Let $\phi$ denote the monomorphism. Then exactness at $FA$ tells us $\ker Fg = \operatorname{im} \phi$. And then maybe it helps if we identify $\operatorname{im} \phi$ with $F(\ker f)$? (Maybe part of my confusion is due to the fact that I'm still used to thinking of kernels and images as objects?) May 21 comment showing exact functors preserve exact sequences (abelian categories, additive functors, and kernels) Hmm, exactness at $F(\ker f)$ means that $F(\ker f) \to FA$ is a monomorphism. Our goal is to show that $\ker Fg = \operatorname{im} Ff$, so we need to extract some information about $\ker Fg$ from the monomorphism $F(\ker f) \to FA$, somehow? Jun 26 comment How to show that this function (related to the zeta function) is even? Sorry, what do you mean by "harmonic sum"? A sum that arises when dealing with Fourier series? Jun 25 comment How to show that this function (related to the zeta function) is even? Wow, thanks! Could you explain how you were able to come up with all of that? Apr 11 comment Transpose of a linear operator on functions Ah, thanks! I was thinking of using the divergence theorem, but I wasn't sure if it was applicable (partly because I didn't know what was the exact space of functions $L$ was acting on). Jan 22 comment Why is $y = \sqrt{x-4}$ a function? and $y = \sqrt{4 - x^2}$ should be a circle @vincentbelkin, I edited my answer. Jan 22 comment Why is $y = \sqrt{x-4}$ a function? and $y = \sqrt{4 - x^2}$ should be a circle @AsafKaragila, thanks! Sep 1 comment Is there a simple way to bound this contour integral? Thanks for your comment. I realized that I was having a hard time phrasing my question. Now that I think about it, I wanted to be able to get a sharper estimation - I wanted to be able to get a feel for how $\int e^{-R^2 \cos2\theta} R \, d\theta$ behaves for large values of $R$ (even though to evaluate the original integral, we just needed to show this was $o(1)$). But like you said, this estimation isn't too bad. How did you get that estimate of yours? Sep 1 comment Bounding a function by its second derivative using Fourier series I am sorry, but I am confused. I am asking if there is a way to bound a function by its second derivative with Fourier series, not when a function has a Fourier series. Aug 9 comment Proving the mean value property of harmonic functions using distributions? Thank you! This was really easy to follow! One question I have is: how do we generalize this argument to higher dimensions? I know the radial component of $\Delta \phi$ will be $\phi_{rr}+\frac{n-1}{r}\phi_r$, but why is the integral of the remaining part zero? Jan 20 comment Fundamental domain for the group of transformations generated by $\tau \mapsto \tau + 2$ and $\tau \mapsto -1/\tau$ Thank you! I had not thought about the structure of $G$ at all. Sep 8 comment How to show that $\lim\limits_{x \to \infty} f'(x) = 0$ implies $\lim\limits_{x \to \infty} \frac{f(x)}{x} = 0$? This is really nice! Thanks! Sep 8 comment How to show that $\lim\limits_{x \to \infty} f'(x) = 0$ implies $\lim\limits_{x \to \infty} \frac{f(x)}{x} = 0$? Wow! This really is an immediate consequence of L'Hopital's rule! Thanks for helping me finish my solution! Aug 9 comment How do I prove the divergence of this series? @Didier: Oh yeah, thanks for pointing that out! Aug 9 comment How do I prove the divergence of this series? @Asaf: Hmm, that's a good point. If the original problem was with $\frac{1}{\log log n}$, I guess my solution was overkill. Jun 8 comment How does the parallelogram law imply the existence of an inner product for a given norm? Thanks! I'm sorry I didn't find that when I searched for this question. May 27 comment Understanding the Schwarz reflection principle Thanks! That was the statement and construction given by the book, and while I could understand it, I didn't understand why my construction didn't work. May 27 comment Understanding the Schwarz reflection principle Thank you! This was exactly my problem! I had assumed that $f(\overline{z})$ was holomorphic because it was a pretty "nice and simple" function. I just started studying complex analysis, so I had the definition of holomorphic memorized without much intution, but I understand the idea a lot better now!