On Orthogonal Polynomials with Regularly Distributed Zeros

In this case the points 0k,, = are sin xkn are equidistributed in Weyl's sense . A non-negative measure da for which the array xkn (da) has the distribution function fl o(t) will be called an arc-sine measure . If du(x) = w(x) dx is absolutely continuous, we apply, replacing dca by w, the notations pn(W,x), yn (w), xkn(w) and call a non-negative w(x) an arc-sine weight if da(x) = w(x) dx is an arc-sine measure. A fairly complete treatise of are-sine weights with compact support is given in [9] by Ullman . The restricted support of a weight w(x) is defined as the set {x : w(x) > 0} . The support of w(x) can be characterized as the set of points e for which