On the norm of the hyperinterpolation operator on the dd-dimensional cube

We obtain the asymptotic order of the operator norm of the hyperinterpolation operator on the cube Id=[−1,1]d,d≥2Id=[−1,1]d,d≥2 with respect to the measure dμ(x)=∏i=1ddxiπ1−xi2. This gives an affirmative answer to a conjecture raised by Caliari et al. (2008).