7 problems

Contour-integral bound conjecture. The remaining contour integral satisfies

Let $\bm{x}$ be a set of unisolvent interpolation points, let $c(\bm{x})$ denote the equioscillating spline associated with these points, let $I(1)$ denote the integral of the cons…

Let $\Omega\subset\mathbb{R}^d$ be a compact subset, let $\mu$ be a finite measure on $\Omega$, and let $X_N$ be an $N$-dimensional subspace of the real space $L_2(\Omega,\mu)$ who…

Let $\Gamma$ be an analytic curve, and let $R$ denote the radius of curvature at a point of highest curvature on $\Gamma$. A Schwarz singularity is a singularity of the analytic co…

Exponential quadrature-error conjecture. The quadrature error for the exponential function satisfies

Quadrature-error conjecture. The quadrature error satisfies

Relative-accuracy conjecture. The coordinates of $\beta^{(n)}$ satisfy, for every $1\leq k\leq N$,