interpolant has the variation diminishning property. Moreover, for low order B-spline interpolation, it can be shown that $\kappa_\infty(A)$ is bounded *independently* of the knot sequence [@deBoor-2001].

On these grounds, in 1975, Carl de Boor [@deBoor-75] conjectured that the interpolation by B-splines of degree $d$ at knot averages is bounded by a function that depends only on $d$, regardless of the knots themselves. In our terms, the conjecture says that $\kappa_\infty(A)$ or, equivalently, $\| A^{-1} \|_\infty$ is bounded by a function of $d$ only. The conjecture was disproved by Rong–Qing Jia [@Jia-88] in 1988. He proved that, for geometric meshes, the condition number $\kappa_\infty(A)$ is not bounded independently of the knot sequence, for degrees $d \geq 19$.

Therefore, it is a natural question whether exists any class of meshes for which de Boor’s conjecture is valid. Since geometric meshes are highly nonuniform, the most likely candidates for the validity are uniform meshes.

Here we discuss the problem of interpolation at knot averages by B-splines with *equidistant simple* knots. The corresponding B-splines are symmetric on the support, and have the highest possible smoothness. It is easy to see that the condition of this interpolation does not depend on the knot spacing $h$, 