ABSTRACT
We investigate the construction of cubature formulas for the unit sphere in https://www.w3.org/1998/Math/MathML"> R n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003419839/4baaeab4-d6e3-45ed-9dec-1deb90c341dd/content/inline-math373.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> that have almost equal weights. The corresponding knots are taken from equidistributed point sets on the sphere. The notion of norming sets in connection with the Markov inequality of spherical harmonics is used in order to provide a general result on uniformly stable cubature formulas. We also present some numerical evidence that there exist stable and almost equally-weighted cubature formulas, if the number of knots is slightly larger than required by the exactness conditions for spherical harmonics of a certain degree.
