On Sectorial L-systems with Shr\"odinger operator

TL;DR

This paper investigates L-systems with sectorial operators, exploring their impedance functions' relation to sectorial Stieltjes functions, and analyzes conditions for sectoriality alignment in main and state space operators, including Schrödinger operators.

Contribution

It provides new conditions linking impedance functions to sectoriality properties of L-systems and analyzes Schrödinger operators within this framework.

Findings

Impedance functions relate to sectorial Stieltjes functions.

Conditions for sectoriality alignment in operators are established.

Connections with the Kato problem on sectorial extensions are discussed.

Abstract

We study L-systems with sectorial main operator and connections of their impedance functions with sectorial Stieltjes and inverse Stieltjes functions. Conditions when the main and state space operators (the main and associated state space operators) of a given L-system have the same or not angle of sectoriality are presented in terms of their impedance functions with discussion provided. Detailed analysis of L-systems with one-dimensional sectorial Shro\"odinger operator on half-line is given as well as connections with the Kato problem on sectorial extensions of sectorial forms. Examples that illustrate the obtained results are presented.