2 problems

Odd-order asymptotic optimality conjecture. The asymptotical optimality property persists for these Gauss-type quadrature formulae also when $r$ is odd.

Let $f(x)$ be a spline satisfying a refinement equation with coefficients $c_j$, dilation factor $\lambda$, and shifts $d_j$, and suppose that $\sum_{j=0}^N c_j=\lambda$. Let…