MathOverflow

The following relates to what is known as the Lebesgue inequality, which gives an error bound for approximating functions under certain linear mappings, and ways to generalize that inequality.
Let $X$ be a normed space and let $Y$ be a finite-dimensional linear subspace of $X$. Let $L:X\to Y$ be a bounded and idempotent linear operator, so that $L(L(f))=L(f)$. Then for every function $P$ in $Y$ and every function $f$ in $X$:...

I have a minor result which I'm sure has come up somewhere before but I can't seem to find it.
Consider a confluent hypergeometric function of the form $$\newcommand{\ff}{{}_1F_1}\ff(b+k;b;z)\textrm{, for }k\in\mathbb{N}.$$Numerical tests suggest that this is always a polynomial of degree $k$ multiplied by an exponential. One can prove this in...

Given a finite separating union-closed family $\mathcal{F}$ of finite sets with universe (the union of all sets in the family) $U(\mathcal{F})$, let $f_x = |\{A \in \mathcal{F}: x \in A\}|$ (the frequency of $x$). Separating means that for every two...

$\DeclareMathOperator\ice{ice}\DeclareMathOperator\sice{sice}\DeclareMathOperator\ind{ind}\DeclareMathOperator\Dio{Dio}\DeclareMathOperator\len{len}$
Context
Let $(X, \sigma)$ be a minimal subshift which is the natural encoding