Orthogonal polynomials on the real line corresponding to a perturbed chain sequence

Abstract

In recent years, chain sequences and their perturbations have played a significant role in characterising the orthogonal polynomials both on the real line as well as on the unit circle. In this note, a particular disturbance of the chain sequence related to orthogonal polynomials having their true interval of orthogonality as a subset of $[0,\infty)$ is studied leading to an important consequence related to the kernel polynomials. Such perturbations are shown to be related to transformations of symmetric measures. An illustration using the generalized Laguerre polynomials is also provided.