The c-Entropy optimality of Donoghue classes

TL;DR

This paper investigates the c-Entropy of perturbed L-systems, deriving explicit formulas and analyzing how the entropy behaves with respect to perturbations, especially in relation to Donoghue classes.

Contribution

It provides explicit formulas linking c-Entropy to perturbation parameters and characterizes the maximum entropy conditions for L-systems in Donoghue classes.

Findings

c-Entropy formulas depend on perturbation parameters

Maximum c-Entropy occurs when the impedance function is in Donoghue classes

c-Entropy can be finite or infinite depending on the perturbation

Abstract

In this note we evaluate c-Entropy of perturbed L-systems introduced in [5]. Explicit formulas relating the c-Entropy of the L-systems and the perturbation parameter are established. We also show that c-Entropy attains its maximum value (finite or infinite) whenever the perturbation parameter vanishes so that the impedance function of such a L-system belongs to one of the generalized (or regular) Donoghue classes.