Marek
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 Feb15 comment Summation using residues $\sinh(z)$ has zeros on the imaginary axis. I don't see how you account for them. Feb13 answered Limit sequence sets Feb13 comment $\sum a_n$ converges $\iff \sum (\sqrt{1+a_n}-1)$ converges When $a_n$ is small (a necessary condition for the convergence of the sum), $\sqrt{1 + a_n} = 1 + a_n / 2 + O(a_n^2)$. So, up to a sum over $a_n^2$ (which converges), these sums are similar. Your job is to find precise estimates. Feb13 answered Issue while applying Master Theorem Feb13 comment Issue while applying Master Theorem @chersanya: again, true. But for the function you've written, you can bound $f(n)$ between $n^2 \log n$ and $3 n^2 \log n$. Both of them are regular, and so you can apply the master theorem. Then you get the master theorem for $f(n)$ by sandwiching between these two results (which are equal). Feb13 comment Issue while applying Master Theorem @chersanya: that's true of course, but the additional terms can't spoil the asymptotic behavior (the regularity only needs to hold for $n$ big enough, not for all $n$). So when $n$ is big enough, it's okay (and this can be made rigorous) to assume that $f(n)$ actually is $C n^2 \log(n)$. Feb13 revised How to prove this result about connectedness? Fixed a letter switch Feb13 comment How to prove this result about connectedness? @Stefan: indeed I switched the letters. Thank you :) Feb13 answered Uniform and point wise convergence Feb13 comment Issue while applying Master Theorem Why do you think $f$ is not regular? We have $af(n/b) \leq (5/9) f(n)$. Feb13 answered Homogenous Polynomial Functions and the Symbol of a Differential Operator Feb13 answered How to prove this result about connectedness? Feb13 comment On surjectivity of exponential map for Lie groups Thank you, nice example. Feb12 comment On surjectivity of exponential map for Lie groups @David: correct me if I am wrong, but the sphere is not a local object, is it? I mean, for every point of the sphere, we can find a ball in $\mathfrak g$ around that point it that still maps to an open set. Feb12 revised On surjectivity of exponential map for Lie groups More detailed proof of exp being closed and open Feb12 comment On surjectivity of exponential map for Lie groups @David: thank you for the first example, I'll think about it. As for the second, I don't follow. Where does the set you've given lie and how is it related to the property of local homeomorphism? Feb12 asked On surjectivity of exponential map for Lie groups Feb12 comment Universal Covering Group of $SO(1,3)^{\uparrow}$ Thanks, that's a nice argument. The adjoint rep. won't work in general, but finding any isomorphism of Lie algebras will, so I guess that's good enough. Feb12 comment Universal Covering Group of $SO(1,3)^{\uparrow}$ I'd say it's purely coincidental and follows from identification of vectors and antisymmetric matrices in dimensions $3$. In any case, could you elaborate how does the adjoint rep. of $su(2)$ help us prove that $SU(2)$ is a universal cover of $SO(3)$? Feb11 comment Limit of $\epsilon t-f(t)$ Are you sure this a correct statement of the problem? If a function $\epsilon t - f(t)$ is unbounded on $[0, \infty]$ then your limit is infinite by definition of unbounded.