Sectorial classes of inverse Stieltjes functions and \(L\)-systems. (English) Zbl 1258.47019

The authors study operator colligations whose state-space operators considered in appropriate rigged Hilbert spaces are sectorial. They introduce classes of matrix-valued functions realized as impedance functions of colligations of the above type, as well as related classes of scalar functions. The angle of sectoriality is expressed in terms of limit values of the impedance function. Examples based on the Schrödinger operator on half-line are given.


47A48 Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc.
93B28 Operator-theoretic methods
47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
47N70 Applications of operator theory in systems, signals, circuits, and control theory