A lower bound for the norm of the periodic error functional

For the effectiveness of the cubature formula, it is necessary that the norm of the error functional be minimal. To minimize the norm of the functional, a sequence of finite functions is constructed on the basis of averaging the characteristic function of a domain with a piecewise-smooth boundary. In this article, using the properties of an extremal function, we obtain a lower bound for the norm of the error functional for cubature formulas with nodes on parallelepiped lattices in an anisotropic space.