Abstract:
The element of the uniformly convex space on which a functional reaches its norm is constructed. The result finds an application in the theory of cubature formulas where the error of numerical integration is represented by a linear functional and may be estimated via its norm. The norm of the error functional is expressed through such element which is called an extreme function.
Keywords:extreme function, weighted Sobolev space, linear compactly supported functional, integral representation of a functional, norm of a functional, norm of an extreme function.