Abstract: The asymptotic behavior of the best
one-sided-approximation of the kernels by algebraic polynomials is
obtained. Between the best one-sided approximation and the quadrature formula
exists a closed relationship used in particular to prove the uniqueness of the
element of the best one-sided approximation and the lower estimate of the
element of the best one-sided approximation in the space
Keywords and phrases: approximation by algebraic polynomials, best one-sided approximation, Spline, Favard constant, truncated power, asymptotic equations.
