Multiplication operator on a matrix polynomial

Abstract

It is proved that the study of a perturbed multiplication operator on a matrix polynomial in the space $L_2 (\mathbb{R}, \mathbb{C}^n)$ may be reduced to the study of a perturbed multiplication operator with independent variable in the space $L_2 (\mathbb{R}, \omega, \mathbb{C}^N)$ with weight $\omega$ satisfying the Mackenhaupt condition.