The following theorem links the Fejér-problem directly with the
existence problem
of multivariate Gauss-quadratures and in case of with the existence
of a 2*m*-design.

Thus, for , there exist no Gauss-quadratures for and
for , they do not exist for .
There might be Gauss-quadratures for *m*=2.
But even in these cases it turns out that certain restrictions have to hold.

That is, existence is possible for and it is known for .

Thu Dec 23 19:39:35 CET 1999