On the norm of the hyperinterpolation operator on the d d -dimensional cube ?
We obtain the asymptotic order of the operator norm of the hyperinterpolation operator on the cube Id=[?1,1]d,d?2 I d = [ ? 1 , 1 ] d , d ? 2 with respect to the measure d ? ( x ) = ? i = 1 d d x i ? 1 ? x i 2 . This gives an affirmative answer to a conjecture raised by Caliari etal.(2008).
hyperinterpolation operator norm projection regular condition