7 problems

Erdős's conjecture. The Chebyshev nodes are asymptotically optimal for the integral of $\lambda$, so that

Let $MP_n$ be the Morrow-Patterson points for positive integer $n$, and let $\Lambda_n^{MP}$ denote the corresponding Lebesgue constant. Interpolation at $MP_n$ can be interpreted…

Hesthaven's conjecture.

Let the Morrow–Patterson points be the interpolation points on the square supporting a minimal positive cubature formula with $N$ nodes of degree of exactness $2n$ for the product…

Calvi–Phung's conjecture. For every $N\geq1$,

Let $\mathrm{Lisa}_{n,p}$ denote the Lisa point set used for bivariate Lagrange interpolation, and let $L_\mathcal{A}$ be its fundamental Lagrange polynomials. Its Lebesgue constan…

Let $C^d=[-1,1]^d$ be the unit cube, and let $\lambda_{n,d}^*$ denote the optimal Lebesgue constant for total-degree polynomial interpolation of degree $n$ in dimension $d$. For…