Zeros of polynomials orthogonal on several intervals
Abstract
Description
First a formula for the number of zeros of the orthogonal polynomial in the intervals is presented. Then a criteria about the appearance of a zero in a gap is given. Finally a necessary and sufficient condition is derived such that the zeros of the orthogonal polynomials have given accumulation points in the gaps. As a consequence it follows that every point from the gaps is an accumulation point of the zeros of the orthogonal polynomials, if the harmonic measures of the intervals are linearly independent over the rationals. If the harmonic measures are rational then there is a finite number of accumulation points only.
21pages, revised and extended version, slight corrections also
21pages, revised and extended version, slight corrections also