Cubature formulas that are exact for trigonometric polynomials (Q1571194)

The known lower bound for the number of nodes of a cubature formula for integrals is obtained that is exact for trigonometric polynomials of degree no higher than \(2k+1\). A theorem is proved that provides the necessary and sufficient condition for the existence of a special type of cubature formula that is exact for trigonometric polynomials of degree no higher than \(2k+1\) and has the number of nodes equal to the lower bound.