5 problems

Let $l_{1},\ldots,l_{m}$ be straight lines in $\mathbb{R}^{n}$, and let $\mathcal{R}(\mathbf{a}^{1},\ldots,\mathbf{a}^{r})$ be the class of ridge functions determined by $r\geq 3$…

Proximinality conjecture. The space $\mathcal{R}_{b}(X)$ is proximinal in $B(X)$ and, when $X$ is compact, the space $\mathcal{R}_{c}(X)$ is proximinal in $C(X)$ if and only if the…

A multivariate function is represented as a sum of arbitrarily behaved ridge functions, where the function belongs to a certain smoothness class. Smoothness-preserving ridge-functi…

Let $B_{\mathbb R^d}$ denote the unit ball in $\mathbb R^d$, and consider ridge functions of the form … where $a\in\mathbb R^d$ satisfies $\|a\|_{\ell_2^d}=1$ and, for some…

Proximinality criterion. The space $\mathcal{R}_b(X)$ is proximinal in $B(X)$ and the space $\mathcal{R}_c(X)$ is proximinal in $C(X)$ if and only if the lengths of all irreducible…