(The) dirac measure perturbation of quasi-definite moment functionals

Abstract

The weight functions of an orthogonal polynomials with finitely many mass points are studied, since that makes it possible that most of properties in regarding orthogonal polynomials can be compared by the point mass difference on a original weight function. In this paper, in particular, It is found that the regularity of a new orthogonal polynomials is preserved from the original one and there is a close relationships between the zeros of orthogonal polynomials and true interval of orthogonality. And, moreover, the semi-classical ortogonality of the new polynomial system is naturally preserved and we can chracterize the semi-classical ortogonality of new orthogonal polynomials from the original orthogonal polynomials from the original orthogonal polynomial and the degrees of perturbations.