Orthogonal Polynomials.

The purpose of the present paper is to improve some results on orthogonal polynomials, Christoffel functions, orthogonal Fourier series, eigenvalues of Toeplitz matrices and Lagrange interpolation. In particular, the problem is of there being any weight w with compact support such that for each p2 the Lagrange interpolating polynomials corresponding to w diverge in Lpw for some continuous function f will be answered. Most of the paper deals with Christoffel functions and their applications. Many limit relations for orthogonal polynomials are found in the assumption that the coefficients in the recursion formula behave nicely.