Characteristic function of pencils. Model representations of a quadratic operator pencil

TL;DR

This paper introduces a new notion of open systems of second order, derives their characteristic functions, and provides model representations for quadratic non-self-adjoint operator pencils, advancing the mathematical understanding of such systems.

Contribution

It presents a novel concept of open second-order systems, derives their characteristic functions, and constructs model representations for quadratic non-self-adjoint operator pencils.

Findings

Introduced the notion of open second-order systems.

Derived the characteristic function for these systems.

Constructed model representations for quadratic non-self-adjoint operator pencils.

Abstract

Notion of an open system of second order is introduced. Characteristic function for such an open system is obtained. Model representations of a quadratic non-self-adjoint operator pencil are found.