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 Sep 14 comment Explicit construction of a basis in a finite dimensional vector space Yes, but I was looking for an explicit formula. The solution linked to by @AJStas gives the answer. Thanks! Sep 14 asked Explicit construction of a basis in a finite dimensional vector space Aug 22 awarded Revival Apr 11 awarded Yearling Jul 2 awarded Curious Jun 23 awarded Organizer Jun 23 comment An inequality between integrals of series of characteristic functions of cubes There was a very similar question answered here: math.stackexchange.com/questions/807426/… I would like to know if one could do this for $p<1$ Jun 23 revised An inequality between integrals of series of characteristic functions of cubes harmonic analysis is more appropriate here than just "analysis" Jun 23 suggested approved edit on An inequality between integrals of series of characteristic functions of cubes May 15 answered An analysis qual problem Apr 11 awarded Yearling Mar 16 comment Prove that the Laplacian of the integral of a certain function is $0$ This is essentially the Poisson extension: en.wikipedia.org/wiki/Poisson_kernel Mar 16 comment Prove that the Laplacian of the integral of a certain function is $0$ Are you missing a $y$ on the numerator? Feb 16 comment For what values of $p>0, \quad \int^{1}_{0} \frac{x}{\sin{(x^{p})}} \operatorname d\!x$ converges? There isn't any oscillation near $0$ to prevent the integral to blowing up as you make $t$ apporach $0$. So my guess is that this exists whenever $0< p <2$ and diverges for all $p \geq 2$. That this blows up for $p\geq 2$ can easily be proved using the estimate $\sin(x) \leq x$. That it converges for \$0