Vector hyperinterpolation on the sphere Original Research Article

We present new results on hyperinterpolation for spherical vector fields. Especially we consider the operator View the MathML sourceLn, which may be described as an approximation to the L2L2 orthogonal projection View the MathML sourcePn. In detail, we prove that View the MathML sourcePn is the projection with the least uniform norm and that View the MathML sourceLn 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.