Exponential polynomials of least deviation from zero and optimal quadrature formulas

Certain properties of polynomials of exponential functions of least deviation from zero in mean on a segment are established. The dependence of the norm of the extremal polynomial and its roots on the length of the segment is investigated first. On the basis of these properties optimality of equidistant nodes is established in the problem of the best quadrature formula for periodic classes which are prescribed by a constraint on the action of a linear differential operator with real eigenvalues. Formulas for determining the weights of the optimal quadrature formula and a relation for optimal error are presented.
Bibliography: 12 titles.