Henry Shearman
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 Mar9 awarded Popular Question May3 comment Characterisation of the spectrum of certain unitary representations on $L^2(G)$ If it helps, I am mostly concerned with translation operators such as the left and right regular representations. May3 revised Characterisation of the spectrum of certain unitary representations on $L^2(G)$ edited title May3 asked Characterisation of the spectrum of certain unitary representations on $L^2(G)$ Dec5 awarded Yearling Feb20 comment Proof that $n^3+2n$ is divisible by 3 Try expanding $(n+1)^3 + 2(n+1)$ and note that you have assumed $n^3 +2n$ is assumed divisible by 3. What does this tell you about the $n+1$th case? Jan31 revised prove for all $n\geq 0$ that $3 \mid n^3+6n^2+11n+6$ Latex Edit Jan31 suggested approved edit on prove for all $n\geq 0$ that $3 \mid n^3+6n^2+11n+6$ Jan31 comment prove for all $n\geq 0$ that $3 \mid n^3+6n^2+11n+6$ Induction will be handy here. Jan30 comment An open ball is an open set Shouldn't the last part of the inequality be $d(x,y)+d(y,x_0) < r_1+ d(y,x_0) = r$? Jan25 revised Cauchy's convergence criterion added 32 characters in body Jan25 answered Cauchy's convergence criterion Jan24 comment Alternate definition of closed set in $\mathbb{R}$ @JonasMeyer: It's a bit of an abuse of the function notation (or maybe just wrong). I was trying to say that some sort of structure should be shown with $\mathbb{R}$ in the space where the dot was placed just so the community knows whether the OP is dealing in a metric space or a strictly topological space. Sorry for the confusion/bad notation. Jan24 comment Alternate definition of closed set in $\mathbb{R}$ Yes, the standard topology on $\mathbb{R}$ is what would be assumed. I was more implying that it should have been stated that it was a metric space. The balls make that obvious here though. Jan24 comment Alternate definition of closed set in $\mathbb{R}$ It helps if you specify the topological structure of $(\mathbb{R},\cdot)$ in the question. Jan23 comment Convergence of $\sum_{n=1}^\infty\frac{1}{2\cdot n}$ You'll have a hard time with that one. If you factor out the half, then you are left with the harmonic series. Jan23 comment Closure of $A \subset \mathbb{R}$ Ah yes, sorry about that. To ammend the proof strategy that I have provided, you must assume that an element of $bdry(A)$ is either a limit point or an isolated point of both $A$ and $X\backslash A$ and then argue for both cases that it cannot be an interior point. Jan23 comment Closure of $A \subset \mathbb{R}$ $bdry(A)$ is the set of limit points of $A$ that are also limit points of $X\backslash A$. Then you need to show that a boundry point is an element of $\bar{A}$ that cannot be an interior point. Hence from $bdry(A) = \bar{A}\backslash int{A}$, the result follows. Jan20 comment Linear operator's linearity The $z^2$ vanishes with the choice of $a$. Jan20 comment Linear operator's linearity Yes, don't mind me. I confused myself for a second.