Brauer and Geršgorin Locations of Zeros of Perturbed Chebyshev Polynomials of the Second Kind by Dilation

Abstract

We consider some perturbations of Chebyshev polynomials of the second kind obtained by modifying by dilation one of its recurrence coefficients at an arbitrary order. By applying Brauer and Geršgorin theorems to Jacobi matrices associated with such perturbed sequences we obtain some locations of their zeros.