Aran Komatsuzaki
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 Oct 10 comment If $f\in C^{\infty}$, $f$ is in Schwarz space iff $x^{\beta}\partial^{\alpha}f$ is bounded for $\forall \alpha, \beta$. Thanks for your clarification! I think $\delta^{-1}\geq 1$, so the last term can be just modified $2^N\to 2^{N+1}$ as well. Oct 10 accepted If $f\in C^{\infty}$, $f$ is in Schwarz space iff $x^{\beta}\partial^{\alpha}f$ is bounded for $\forall \alpha, \beta$. Oct 10 asked If $f\in C^{\infty}$, $f$ is in Schwarz space iff $x^{\beta}\partial^{\alpha}f$ is bounded for $\forall \alpha, \beta$. Oct 4 comment Why is the number of components of Lie group finite? Thanks for your answer! That solved my question. Oct 4 asked Why is the number of components of Lie group finite? Oct 2 comment Alternative proof for dominated convergence theorem without using Fatou's lemma? Thanks for your remark! But sorry for confusion. When I wrote "after showing that $f_n\to f\in L^1$", I meant that "after showing that $f\in L^1$ where $f_n\to f$ pointwisely. So, probably there isn't any simplistic proof without Fatou's lemma. Oct 2 asked Alternative proof for dominated convergence theorem without using Fatou's lemma? Sep 7 comment What theorem of Sturm-Liouville theory guarantees that the complete solution of heat equation is the linear combination of $\sin nx$? That completely solved my question! Sep 6 asked What theorem of Sturm-Liouville theory guarantees that the complete solution of heat equation is the linear combination of $\sin nx$? Jul 12 awarded Yearling May 27 comment Why does $D \det(I)B=\frac{d}{d t}\det(I+t B)|_{t=0}$ hold? Yes. The one you linked here :-) May 27 comment Why does $D \det(I)B=\frac{d}{d t}\det(I+t B)|_{t=0}$ hold? Eq. (7) looks so interesting! I enjoyed reading your argument in another post where you answered to that question. May 27 comment Why does $D \det(I)B=\frac{d}{d t}\det(I+t B)|_{t=0}$ hold? Thanks for your concise answer! May 27 accepted Why does $D \det(I)B=\frac{d}{d t}\det(I+t B)|_{t=0}$ hold? May 26 comment How does the solution of ODE $y'=F(t,y)$ extend to an open interval? Thanks for a clear answer! May 26 accepted How does the solution of ODE $y'=F(t,y)$ extend to an open interval? May 26 revised How does the solution of ODE $y'=F(t,y)$ extend to an open interval? deleted 286 characters in body May 26 comment How does the solution of ODE $y'=F(t,y)$ extend to an open interval? I'm sorry, but I can't figure out how to use the definition to solve this problem. May 26 asked How does the solution of ODE $y'=F(t,y)$ extend to an open interval? May 26 comment Why does $D \det(I)B=\frac{d}{d t}\det(I+t B)|_{t=0}$ hold? That makes sense! Thanks for your answer.