On the c-entropy of L-systems with Schrodinger operator

TL;DR

This paper investigates the properties of Schr"odinger L-systems, introducing new concepts of c-entropy and dissipation, and explores dual problems related to these measures for specific classes of operators.

Contribution

It introduces the concepts of c-entropy and dissipation coefficient for Schr"odinger L-systems and analyzes dual problems involving these measures.

Findings

Characterization of Schr"odinger L-systems with given c-entropy and minimal dissipation.

Analysis of dual c-entropy problems for sectorial and extremal operators.

Detailed discussion of dual problems in the context of Schr"odinger L-systems.

Abstract

We study L-systems whose main operators are extensions of one-dimensional half-line Schr\"odinger operators with deficiency indices $(1, 1)$, the Schr\"odinger L-systems. Introducing new concepts of an c-entropy and dissipation coefficient for an L-system we discuss the following dual problems: describe Schr\"odinger L-systems (1) with a given c-entropy and minimal dissipation coefficient, and (2) with a given dissipation coefficient and maximal c-entropy. Also, we analyze in detail the dual c-entropy problems for Schr\"odinger L-systems with sectorial and extremal main operators.