Vector hyperinterpolation on the sphere

We present new results on hyperinterpolation for spherical vector fields. Especially we consider the operator Ln, which may be described as an approximation to the L2L2 orthogonal projection Pn. In detail, we prove that Pn is the projection with the least uniform norm and that Ln has the optimal value for its norm in the C→L2C→L2 setting. These results are already known for the scalar case. In the continuous space setting, we could prove only a sub-optimal bound for the Lebesgue constant of the vector hyperinterpolation operator.