The L-system representation and c-entropy

Abstract

Given a symmetric operator $\dot{A}$ with deficiency indices $(1,1)$ and its self-adjoint extension $A$ in a Hilbert space $\mathcal{H}$, we construct a (unique) L-system with the main operator in $\mathcal{H}$ such that its impedance mapping coincides with the Weyl-Titchmarsh function $M_{(\dot{A},A)}(z)$ or its linear-fractional transformation $M_{(\dot{A},A_{\alpha })}(z)$. Similar L-system constructions are provided for the Weyl-Titchmarsh function $a{M}_{(\dot{A},A)}(z)$ with $a>0$. We also evaluate c-entropy and the main operator dissipation coefficient for the obtained L-systems.

26 pages