MathOverflow

I am studying a family of coefficients $c_{k,j}$ indexed by integers $k\ge j\ge 0$ and an alternating sum that I am trying to get the asymptotic growth of:
\begin{equation}S_j(n):=\sum_{k=j}^{\infty}\frac{(-1)^{k+1}}{k+1}\,c_{k,j}\,(\log n)^{k-j}.\end{equation}...

I'm looking for a name for a property: say that a multigraph $(V, E)$ is xyzzy if the subgraph induced by any pair of vertices is finite. So, only finitely many edges between any pair of vertices.
I am aware that $(V, E)$ is said to be locally finite if the neighbourhood of any vertex is finite; xyzzy is incomparable to that property yet looks a bit like it, morally speaking. Whatchamacallit?...

Let $\Lambda$ be a graded lattice with grading $g:\Lambda \to \mathbb{Z}$. A subset $L$ of $\Lambda$ is a lower set (or down-set or order ideal) if for every $y \in L$ and $x < y$ we have $x \in L$. To every nonempty lower set $L$ we assign an integer...

Let $A, B$ be injective self-adjoint operators, both unbounded, acting on a common Hilbert space, with $D$ core for $B$ and $B(D)$ core for $A$. Is $AB\,\big|_D$ closable?