In this note we prove mean convergence of Lagrange interpolation at the zeros para-orthogonal polynomials for measures on unit circle which do not belong to Szegő’s class. When measure is in class, proved functions disk algebra.

Lagrange multipliers offer a way to find the extrema of an objective function f(x1, x2, . . . , xn) subject to a constraint function g(x1, x2, . . . , xn) = 0; for example, we may wish to maximize a+ b+ c subject to a2 + b2 + c2 = 1. However, there are lots of tiny details that need to be checked in order to completely solve a problem with Lagrange multipliers. On an olympiad the use of Lagrang...