On the c-Entropy of L-Systems with Schrödinger Operator

Abstract

We study L-systems whose main operators are extensions of one-dimensional half-line Schrödinger operators with deficiency indices (1, 1), the Schrödinger L-systems. Introducing new concepts of an c-entropy and dissipation coefficient for an L-system we discuss the following dual problems: describe Schrödinger 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 Schrödinger L-systems with sectorial and extremal main operators.