Multiplication operator and exceptional Jacobi polynomials

Abstract

Below the normalized weighted reciprocal of the Christoffel function with respect to exceptional Jacobi polynomials is investigated. It is proved that it tends to the equilibrium measure of the interval of orthogonality in weak-star sense. The main tool of this study is the multiplication operator and examination of behavior of zeros of the corresponding average characteristic polynomial. Finally, as an application of multiplication operator, location of zeros of certain self-inversive polynomials are examined.