Zeros of Orthogonal Polynomials Generated by Canonical Perturbations on Standard Measure

TL;DR

This paper investigates the zeros of orthogonal polynomials resulting from canonical spectral transformations of measures on the real line, providing an electrostatic interpretation of their behavior.

Contribution

It introduces a new analysis of zeros of orthogonal polynomials under spectral transformations and offers an electrostatic interpretation of their behavior.

Findings

Zeros exhibit specific patterns under spectral transformations

Electrostatic model explains zero distribution

Provides insights into measure perturbations effects

Abstract

In this contribution, the behavior of zeros of orthogonal polynomials associated with canonical linear spectral transformations of measures supported in the real line is analyzed. An electrostatic interpretation of them is given.